Filtered Hirsch Algebras

Details Filtered Hirsch Algebras Filtered Hirsch Algebras

2007-07-16

arxiv.org/abs/0707.2165v11

Mathematics

Algebraic Topology

29 pages, 2 figures, text is edited, a reference is added

Scientific paper

Motivated by the cohomology theory of loop spaces we consider a special class of higher order homotopy commutative differential graded algebras. For such an algebra, $A,$ the filtered Hirsch model is constructed. For $A$ over the integers and $x\in H(A)$ with $x^2=0,$ the symmetric Massey products $^{n},n\geq 3$ (whenever defined) have a finite order, while they are defined and vanish in $H(A\otimes \Bbbk)$ for all $n$ and $\Bbbk$ to be a field of characteristic zero. The Kraines formula $^{p}=-\beta\mathcal{P}_1(x)$ is lifted to $H^*(A\otimes {\mathbb Z}_p).$ Applications for the existence of polynomial generators in the loop homology and for the Hochschild cohomology with the $G$-algebra structure are given.

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