Homotopy algebra of open-closed strings

2006/06/30 by Hiroshige Kajiura, Jim Stasheff
Physics and Astronomy · Mathematics · #hep-th #math.AT #math.QA #msc:18G55 #msc:81T18

paper · pdf · doi:10.2140/gtm.2008.13.229

published as Geom. Topol. Monogr. 13 (2008) 229-259 · This is the version published by Geometry & Topology Monographs on 22 February 2008

arxiv created 2009/04/05 · arxiv updated 2009/12/01

Abstract

This paper is a survey of our previous works on open-closed homotopy algebras, together with geometrical background, especially in terms of compactifications of configuration spaces (one of Fred's specialities) of Riemann surfaces, structures on loop spaces, etc. We newly present Merkulov's geometric A_infty-structure [Internat. Math. Res. Notices (1999) 153--164, arxiv:math/0001007] as a special example of an OCHA. We also recall the relation of open-closed homotopy algebras to various aspects of deformation theory.

Citations

• Frobenius_infinity invariants of homotopy Gerstenhaber algebras I

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