JournalsjncgVol. 4 , No. 2DOI 10.4171/jncg/52

Noncommutative geometry and compactifications of the moduli space of curves

  • Alastair Hamilton

    University of Connecticut, Storrs, USA
Noncommutative geometry and compactifications of the  moduli space of curves  cover

Abstract

In this paper we show that the homology of a certain natural compactification of the moduli space, introduced by Kontsevich in his study of Witten’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 by Kontsevich in his subsequent papers.