Noncommutative geometry and compactifications of the moduli space of curves

@article{Hamilton2007NoncommutativeGA,
  title={Noncommutative geometry and compactifications of the moduli space of curves},
  author={Alastair Hamilton},
  journal={arXiv: Quantum Algebra},
  year={2007}
}
  • A. Hamilton
  • Published 2007
  • Mathematics
  • arXiv: Quantum Algebra
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… Expand
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Classes on Compactifications of the Moduli Space of Curves Through Solutions to the Quantum Master Equation
In this paper we describe a construction which produces classes in compactifications of the moduli space of curves. This construction extends a construction of Kontsevich which produces classes inExpand
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