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Homotopy algebra of open–closed strings

Hiroshige Kajiura and Jim Stasheff

Geometry & Topology Monographs 13 (2008) 229–259

DOI: 10.2140/gtm.2008.13.229

arXiv: hep-th/0606283

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–structure [Internat. Math. Res. Notices (1999) 153–164] as a special example of an OCHA. We also recall the relation of open–closed homotopy algebras to various aspects of deformation theory.

Dedicated to Fred Cohen in honor of his 60th birthday

Keywords

homotopy algebra, moduli spaces of Riemann surfaces, deformation theory

Mathematical Subject Classification

Primary: 18G55

Secondary: 81T18

References
Publication

Received: 31 May 2006
Revised: 22 January 2007
Accepted: 25 January 2007
Published: 22 February 2008

Authors
Hiroshige Kajiura
Research Institute for Mathematical Sciences
Kyoto University
Kyoto 606-8502
Japan
Jim Stasheff
Department of Mathematics
University of Pennsylvania
Philadelphia, PA 19104-6395
USA