Noncommutative geometry and compactifications of the moduli space of curves

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Abstract

In this paper we show that the homology of a certain natural compactification of the moduli space, introduced by Kontsevich in his study ofWitten's conjectures, can be described completely algebraically as the homology of a certain differential graded Lie algebra. This two-parameter family is constructed by using a Lie cobracket on the space of noncommutative 0-forms, a structure which corresponds to pinching simple closed curves on a Riemann surface, to deform the noncommutative symplectic geometry described byKontsevich in his subsequent papers.

Original languageEnglish
Pages (from-to)157-188
Number of pages32
JournalJournal of Noncommutative Geometry
Volume4
Issue number2
DOIs
StatePublished - 2010

Keywords

  • Homology theory
  • Lie bialgebra
  • Moduli spaces
  • Noncommutative geometry

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