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Steenrod operations and Hochshild homology | | Bitjong Ndombol
; Jean-Claude Thomas
; | | Date: |
20 Sep 2001 | | Subject: | Algebraic Topology; Commutative Algebra MSC-class: 55P35, 13D03, 55P48, 16E45, 18F25 | math.AT math.AC | | Abstract: | Let $X$ be a simply connected space and ${Bbb F}_p$ be a prime field. The algebra of normalized singular cochains $N^*(X; {Bbb F}_p)$ admits a natural homotopy structure which induces natural Steenrod operations on the Hochschild homology $HH_* N^*(X;{Bbb F}_p)$ of the space $X$. The primary purpose of this paper is to prove that the J. Jones isomorphism $HH_*N^*(X;{Bbb F}_p) cong H ^*(X^{S^1};{Bbb F}_p)$ identifies theses Stenrood operations with those defined on the cohomology of the free loop space with coefficients in ${Bbb F}_p$. The other goal of this paper is to describe a theoritic model which allows to do some computations. | | Source: | arXiv, math.AT/0109146 | | Services: | Forum | Review | PDF | Favorites | |
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