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arXiv · 2307.10300

Ainfinity-algebra Structure in Cohomology and its Applications

Tornike Kadeishvili
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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.

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Tornike Kadeishvili. 2023-07-18. Ainfinity-algebra Structure in Cohomology and its Applications. https://arxiv.org/abs/2307.10300

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