Recursion Between Mumford Volumes of Moduli Spaces View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2011-12

AUTHORS

Bertrand Eynard

ABSTRACT

We propose a new proof, as well as a generalization of Mirzakhani’s recursion for volumes of moduli spaces. We interpret those recursion relations in terms of expectation values in Kontsevich’s integral, i.e., we relate them to a ribbon graph decomposition of Riemann surfaces. We find a generalization of Mirzakhani’s recursions to measures containing all higher Mumford’s κ classes, and not only κ1 as in the Weil–Petersson case. More... »

PAGES

1431-1447

References to SciGraph publications

  • 1993-01. Polynomial averages in the Kontsevich model in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1978-02. Planar diagrams in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2004-11-12. Topological expansion for the 1-hermitian matrix model correlation functions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-01. Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces in INVENTIONES MATHEMATICAE
  • 1992-06. Intersection theory on the moduli space of curves and the matrix airy function in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1983. Towards an Enumerative Geometry of the Moduli Space of Curves in ARITHMETIC AND GEOMETRY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00023-011-0113-4

    DOI

    http://dx.doi.org/10.1007/s00023-011-0113-4

    DIMENSIONS

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