Classes on the moduli space of Riemann surfaces through a noncommutative Batalin-Vilkovisky formalism

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Abstract

Using the machinery of the Batalin-Vilkovisky formalism, we construct cohomology classes on compactifications of the moduli space of Riemann surfaces from the data of a contractible differential graded Frobenius algebra. We describe how evaluating these cohomology classes upon a well-known construction producing homology classes in the moduli space can be expressed in terms of the Feynman diagram expansion of some functional integral. By computing these integrals for specific examples, we are able to demonstrate that this construction produces families of nontrivial classes.

Original languageEnglish
Pages (from-to)67-101
Number of pages35
JournalAdvances in Mathematics
Volume243
DOIs
StatePublished - Aug 20 2013

Keywords

  • Batalin-Vilkovisky formalism
  • Lie algebra cohomology
  • Moduli space of curves
  • Noncommutative geometry
  • Topological field theory

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