Classes on compactifications of the moduli space of curves through solutions to the quantum master equation

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Abstract

In this paper we describe a construction which produces classes in compactifications of the moduli space of curves. This construction extends a construction of Kontsevich which produces classes in the open moduli space from the initial data of a cyclic A-algebra. The initial data for our construction are what we call a 'quantum A-algebra', which arises as a type of deformation of a cyclic A-algebra. The deformation theory for these structures is described explicitly. We construct a family of examples of quantum A-algebras which extend a family of cyclic A-algebras, introduced by Kontsevich, which are known to produce all the kappa classes using his construction.

Original languageEnglish
Pages (from-to)115-130
Number of pages16
JournalLetters in Mathematical Physics
Volume89
Issue number2
DOIs
StatePublished - Aug 2009

Keywords

  • A-algebra
  • Deformation theory
  • Maurer-Cartan set
  • Moduli space of curves
  • Noncommutative geometry

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