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
