Homotopy algebra of open-closed strings
Hiroshige Kajiura, Jim Stasheff
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 Ainfty-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.
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