English

Ainfinity-algebra Structure in Cohomology and its Applications

Algebraic Topology 2023-07-21 v1

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()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()C(\infty) algebra and the commutatitive version of the minimality theorem by which in rational cohomology algebra appear multioperations which form a C()C(\infty) algebra structure which completely determines the rational homotopy type.

Keywords

Cite

@article{arxiv.2307.10300,
  title  = {Ainfinity-algebra Structure in Cohomology and its Applications},
  author = {Tornike Kadeishvili},
  journal= {arXiv preprint arXiv:2307.10300},
  year   = {2023}
}

Comments

65 pages. arXiv admin note: text overlap with arXiv:0811.1655