Noncommutative geometry and compactifications of the moduli space of curves
Quantum Algebra
2007-10-26 v1 Algebraic Geometry
Algebraic Topology
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.
Keywords
Cite
@article{arxiv.0710.4603,
title = {Noncommutative geometry and compactifications of the moduli space of curves},
author = {Alastair Hamilton},
journal= {arXiv preprint arXiv:0710.4603},
year = {2007}
}
Comments
23 pages, 10 figures