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Classes on Compactifications of the Moduli Space of Curves Through Solutions to the Quantum Master Equation.
- Source :
- Letters in Mathematical Physics; Aug2009, Vol. 89 Issue 2, p115-130, 16p
- Publication Year :
- 2009
-
Abstract
- 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<subscript>∞</subscript>-algebra. The initial data for our construction are what we call a ‘quantum A<subscript>∞</subscript>-algebra’, which arises as a type of deformation of a cyclic A<subscript>∞</subscript>-algebra. The deformation theory for these structures is described explicitly. We construct a family of examples of quantum A<subscript>∞</subscript>-algebras which extend a family of cyclic A<subscript>∞</subscript>-algebras, introduced by Kontsevich, which are known to produce all the kappa classes using his construction. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03779017
- Volume :
- 89
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Letters in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 44868260
- Full Text :
- https://doi.org/10.1007/s11005-009-0310-y