Classes on Compactifications of the Moduli Space of Curves Through Solutions to the Quantum Master Equation

@article{Hamilton2009ClassesOC,
  title={Classes on Compactifications of the Moduli Space of Curves Through Solutions to the Quantum Master Equation},
  author={Alastair Hamilton},
  journal={Letters in Mathematical Physics},
  year={2009},
  volume={89},
  pages={115-130}
}
  • A. Hamilton
  • Published 14 July 2008
  • Mathematics
  • Letters in Mathematical Physics
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 in the open moduli space from the initial data of a cyclic A∞-algebra. The initial data for our construction are what we call a ‘quantum A∞-algebra’, which arises as a type of deformation of a cyclic A∞-algebra. The deformation theory for these structures is described explicitly. We construct a family of… 
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