Ainfinity-algebra Structure in Cohomology and its Applications

Abstract

In these lectures we present our minimality theorem by which in cohomology of a topological space appear multioperations which turn it ot Stasheff $A(\infty)$ algebra. This rich structure carries more information than just the structure of cohomology algebra, particularly it allows to define cohomologies of the loop space. We present also the notion of $C(\infty)$ algebra and the commutatitive version of the minimality theorem by which in rational cohomology algebra appear multioperations which form a $C(\infty)$ algebra structure which completely determines the rational homotopy type.