NONCOMMUTATIVE HOMOTOPY ALGEBRAS ASSOCIATED WITH OPEN STRINGS
NONCOMMUTATIVE HOMOTOPY ALGEBRAS ASSOCIATED WITH OPEN STRINGS
We discuss general properties of $A_\infty$-algebras and their applications to the theory of open strings. The properties of cyclicity for $A_\infty$-algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for $A_\infty$-algebras and cyclic $A_\infty$-algebras and discuss various consequences of …