Analysis of S2-Valued Maps and Faddeev’s Model View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2005-06

AUTHORS

Dave Auckly, Lev Kapitanski

ABSTRACT

In this paper we consider a generalization of the Faddeev model for the maps from a closed three-manifold into the two-sphere. We give a novel representation of smooth S2-valued maps based on flat connections. This representation allows us to obtain an analytic description of the homotopy classes of S2-valued maps that generalizes to Sobolev maps. It also leads to a new proof of an old theorem of Pontrjagin. For the generalized Faddeev model, we prove the existence of minimizers in every homotopy class. More... »

PAGES

611-620

References to SciGraph publications

  • 1931-12. Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche in MATHEMATISCHE ANNALEN
  • 2006-04. Fermionic Quantization and Configuration Spaces for the Skyrme and Faddeev-Hopf Models in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2002. On Skyrme’s Model in NONLINEAR PROBLEMS IN MATHEMATICAL PHYSICS AND RELATED TOPICS II
  • 1997-05. Stable knot-like structures in classical field theory in NATURE
  • 1982. Differential Forms in Algebraic Topology in NONE
  • 2003-09. Holonomy and Skyrme's Model in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00220-005-1289-6

    DOI

    http://dx.doi.org/10.1007/s00220-005-1289-6

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1037389054


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Kansas State University", 
              "id": "https://www.grid.ac/institutes/grid.36567.31", 
              "name": [
                "Department of Mathematics, Kansas State University, 66506, Manhattan, KS, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Auckly", 
            "givenName": "Dave", 
            "id": "sg:person.012632611137.94", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012632611137.94"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Miami", 
              "id": "https://www.grid.ac/institutes/grid.26790.3a", 
              "name": [
                "Department of Mathematics, University of Miami, 33124, Coral Gables, FL, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Kapitanski", 
            "givenName": "Lev", 
            "id": "sg:person.01041775714.71", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01041775714.71"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s00220-005-1496-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002741000", 
              "https://doi.org/10.1007/s00220-005-1496-1"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9947-1987-0902788-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1014306039"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01457962", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015430180", 
              "https://doi.org/10.1007/bf01457962"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01457962", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015430180", 
              "https://doi.org/10.1007/bf01457962"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0029-5582(62)90775-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019864545"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0029-5582(62)90775-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019864545"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1098/rsta.2001.0842", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033334456"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1098/rspa.1961.0018", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037916716"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1038/387058a0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1039400235", 
              "https://doi.org/10.1038/387058a0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1043294424", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4757-3951-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043294424", 
              "https://doi.org/10.1007/978-1-4757-3951-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4757-3951-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043294424", 
              "https://doi.org/10.1007/978-1-4757-3951-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00220-003-0901-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044623916", 
              "https://doi.org/10.1007/s00220-003-0901-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1142/s0217751x88001156", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1062928630"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4615-0701-7_13", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1089530288", 
              "https://doi.org/10.1007/978-1-4615-0701-7_13"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2005-06", 
        "datePublishedReg": "2005-06-01", 
        "description": "In this paper we consider a generalization of the Faddeev model for the maps from a closed three-manifold into the two-sphere. We give a novel representation of smooth S2-valued maps based on flat connections. This representation allows us to obtain an analytic description of the homotopy classes of S2-valued maps that generalizes to Sobolev maps. It also leads to a new proof of an old theorem of Pontrjagin. For the generalized Faddeev model, we prove the existence of minimizers in every homotopy class.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s00220-005-1289-6", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136216", 
            "issn": [
              "0010-3616", 
              "1432-0916"
            ], 
            "name": "Communications in Mathematical Physics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "256"
          }
        ], 
        "name": "Analysis of S2-Valued Maps and Faddeev\u2019s Model", 
        "pagination": "611-620", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "b21afbe74e5f395f483e4201024a7105bdc648f6ee9470b156ac5f182c883370"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00220-005-1289-6"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1037389054"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00220-005-1289-6", 
          "https://app.dimensions.ai/details/publication/pub.1037389054"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T14:32", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000373_0000000373/records_13102_00000001.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007%2Fs00220-005-1289-6"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00220-005-1289-6'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00220-005-1289-6'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00220-005-1289-6'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00220-005-1289-6'


     

    This table displays all metadata directly associated to this object as RDF triples.

    112 TRIPLES      21 PREDICATES      39 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00220-005-1289-6 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N411f36f1195243648bbb19021d319e69
    4 schema:citation sg:pub.10.1007/978-1-4615-0701-7_13
    5 sg:pub.10.1007/978-1-4757-3951-0
    6 sg:pub.10.1007/bf01457962
    7 sg:pub.10.1007/s00220-003-0901-x
    8 sg:pub.10.1007/s00220-005-1496-1
    9 sg:pub.10.1038/387058a0
    10 https://app.dimensions.ai/details/publication/pub.1043294424
    11 https://doi.org/10.1016/0029-5582(62)90775-7
    12 https://doi.org/10.1090/s0002-9947-1987-0902788-8
    13 https://doi.org/10.1098/rspa.1961.0018
    14 https://doi.org/10.1098/rsta.2001.0842
    15 https://doi.org/10.1142/s0217751x88001156
    16 schema:datePublished 2005-06
    17 schema:datePublishedReg 2005-06-01
    18 schema:description In this paper we consider a generalization of the Faddeev model for the maps from a closed three-manifold into the two-sphere. We give a novel representation of smooth S2-valued maps based on flat connections. This representation allows us to obtain an analytic description of the homotopy classes of S2-valued maps that generalizes to Sobolev maps. It also leads to a new proof of an old theorem of Pontrjagin. For the generalized Faddeev model, we prove the existence of minimizers in every homotopy class.
    19 schema:genre research_article
    20 schema:inLanguage en
    21 schema:isAccessibleForFree false
    22 schema:isPartOf N7b2e5107f2024af39911a8e7746ebd63
    23 Na61c514394444442aecfd23831416623
    24 sg:journal.1136216
    25 schema:name Analysis of S2-Valued Maps and Faddeev’s Model
    26 schema:pagination 611-620
    27 schema:productId N5923de4fca4649df92d70fb7c1c3b915
    28 Nc5e65cd07e8e4419ac62e79080e4c927
    29 Ne4917e3761e4431d95167f8503f57de2
    30 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037389054
    31 https://doi.org/10.1007/s00220-005-1289-6
    32 schema:sdDatePublished 2019-04-11T14:32
    33 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    34 schema:sdPublisher N17b477b1757643af8f25a985423fc073
    35 schema:url http://link.springer.com/10.1007%2Fs00220-005-1289-6
    36 sgo:license sg:explorer/license/
    37 sgo:sdDataset articles
    38 rdf:type schema:ScholarlyArticle
    39 N17b477b1757643af8f25a985423fc073 schema:name Springer Nature - SN SciGraph project
    40 rdf:type schema:Organization
    41 N411f36f1195243648bbb19021d319e69 rdf:first sg:person.012632611137.94
    42 rdf:rest Nc218d7387fe8494490ae4574a1b85ed5
    43 N5923de4fca4649df92d70fb7c1c3b915 schema:name doi
    44 schema:value 10.1007/s00220-005-1289-6
    45 rdf:type schema:PropertyValue
    46 N7b2e5107f2024af39911a8e7746ebd63 schema:volumeNumber 256
    47 rdf:type schema:PublicationVolume
    48 Na61c514394444442aecfd23831416623 schema:issueNumber 3
    49 rdf:type schema:PublicationIssue
    50 Nc218d7387fe8494490ae4574a1b85ed5 rdf:first sg:person.01041775714.71
    51 rdf:rest rdf:nil
    52 Nc5e65cd07e8e4419ac62e79080e4c927 schema:name readcube_id
    53 schema:value b21afbe74e5f395f483e4201024a7105bdc648f6ee9470b156ac5f182c883370
    54 rdf:type schema:PropertyValue
    55 Ne4917e3761e4431d95167f8503f57de2 schema:name dimensions_id
    56 schema:value pub.1037389054
    57 rdf:type schema:PropertyValue
    58 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    59 schema:name Mathematical Sciences
    60 rdf:type schema:DefinedTerm
    61 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    62 schema:name Pure Mathematics
    63 rdf:type schema:DefinedTerm
    64 sg:journal.1136216 schema:issn 0010-3616
    65 1432-0916
    66 schema:name Communications in Mathematical Physics
    67 rdf:type schema:Periodical
    68 sg:person.01041775714.71 schema:affiliation https://www.grid.ac/institutes/grid.26790.3a
    69 schema:familyName Kapitanski
    70 schema:givenName Lev
    71 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01041775714.71
    72 rdf:type schema:Person
    73 sg:person.012632611137.94 schema:affiliation https://www.grid.ac/institutes/grid.36567.31
    74 schema:familyName Auckly
    75 schema:givenName Dave
    76 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012632611137.94
    77 rdf:type schema:Person
    78 sg:pub.10.1007/978-1-4615-0701-7_13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089530288
    79 https://doi.org/10.1007/978-1-4615-0701-7_13
    80 rdf:type schema:CreativeWork
    81 sg:pub.10.1007/978-1-4757-3951-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043294424
    82 https://doi.org/10.1007/978-1-4757-3951-0
    83 rdf:type schema:CreativeWork
    84 sg:pub.10.1007/bf01457962 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015430180
    85 https://doi.org/10.1007/bf01457962
    86 rdf:type schema:CreativeWork
    87 sg:pub.10.1007/s00220-003-0901-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1044623916
    88 https://doi.org/10.1007/s00220-003-0901-x
    89 rdf:type schema:CreativeWork
    90 sg:pub.10.1007/s00220-005-1496-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002741000
    91 https://doi.org/10.1007/s00220-005-1496-1
    92 rdf:type schema:CreativeWork
    93 sg:pub.10.1038/387058a0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039400235
    94 https://doi.org/10.1038/387058a0
    95 rdf:type schema:CreativeWork
    96 https://app.dimensions.ai/details/publication/pub.1043294424 schema:CreativeWork
    97 https://doi.org/10.1016/0029-5582(62)90775-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019864545
    98 rdf:type schema:CreativeWork
    99 https://doi.org/10.1090/s0002-9947-1987-0902788-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014306039
    100 rdf:type schema:CreativeWork
    101 https://doi.org/10.1098/rspa.1961.0018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037916716
    102 rdf:type schema:CreativeWork
    103 https://doi.org/10.1098/rsta.2001.0842 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033334456
    104 rdf:type schema:CreativeWork
    105 https://doi.org/10.1142/s0217751x88001156 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062928630
    106 rdf:type schema:CreativeWork
    107 https://www.grid.ac/institutes/grid.26790.3a schema:alternateName University of Miami
    108 schema:name Department of Mathematics, University of Miami, 33124, Coral Gables, FL, USA
    109 rdf:type schema:Organization
    110 https://www.grid.ac/institutes/grid.36567.31 schema:alternateName Kansas State University
    111 schema:name Department of Mathematics, Kansas State University, 66506, Manhattan, KS, USA
    112 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...