Noncommutative geometry and compactifications of the moduli space of curves

Details Noncommutative geometry and compactifications of the moduli space of curves Noncommutative geometry and compactifications of the moduli space of curves

2007-10-25

arxiv.org/abs/0710.4603v1

Mathematics

Quantum Algebra

23 pages, 10 figures

Scientific paper

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.

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