Axioms for the fixed point index of n-valued maps, and some applications View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-06

AUTHORS

P. Christopher Staecker

ABSTRACT

We give an axiomatic characterization of the fixed point index of an n-valued map. For n-valued maps on a polyhedron, the fixed point index is shown to be unique with respect to axioms of homotopy invariance, additivity, and a splitting property. This uniqueness is used to obtain easy proofs of an averaging formula and product formula for the index. In the setting of n-valued maps on a manifold, we show that the axioms can be weakened. More... »

PAGES

61

References to SciGraph publications

  • 2009-08. Axioms for a local Reidemeister trace in fixed point and coincidence theory on differentiable manifolds in JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
  • 2004-12. On the uniqueness of the fixed point index on differentiable manifolds in FIXED POINT THEORY AND APPLICATIONS
  • 2015-03. Lefschetz indices for n-valued maps in JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
  • 2004-12. The Lefschetz-Hopf theorem and axioms for the Lefschetz number in FIXED POINT THEORY AND APPLICATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11784-018-0543-4

    DOI

    http://dx.doi.org/10.1007/s11784-018-0543-4

    DIMENSIONS

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