English

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