Classes on compactifications of the moduli space of curves through solutions to the quantum master equation

Details Classes on compactifications of the moduli space of curves through solutions to the quantum master equation Classes on compactifications of the moduli space of curves through solutions to the quantum master equation

2008-07-14

arxiv.org/abs/0807.2270v3

Mathematics

Quantum Algebra

This version includes an updated list of references

Scientific paper

10.1007/s11005-009-0310-y

In this paper we describe a construction which produces classes in a compactification 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-infinity algebra. The initial data for our construction is what we call a `quantum A-infinity algebra', which arises as a type of deformation of a cyclic A-infinity algebra. The deformation theory for these structures is described explicitly. We construct a family of examples of quantum A-infinity algebras which extend a family of cyclic A-infinity algebras, introduced by Kontsevich, which are known to produce all the Miller-Morita-Mumford classes using his construction.

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