2001/09/20 by Bitjong Ndombol, Ndombol, Bitjong, Jean-Claude Thomas +1
Mathematics · #13D03 #16E45 #18F25 #55P35 #55P48 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AT #msc:13D03 #msc:16E45 #msc:18F25 #msc:55P35 #msc:55P48
paper · pdf · doi:10.48550/arxiv.math/0109146
20 pages
arxiv created 2001/09/20 · arxiv updated 2009/11/30
Let X be a simply connected space and \Bbb Fp be a prime field. The algebra of normalized singular cochains N^*(X; \Bbb Fp) admits a natural homotopy structure which induces natural Steenrod operations on the Hochschild homology HH_* N^*(X;\Bbb Fp) of the space X. The primary purpose of this paper is to prove that the J. Jones isomorphism HH_*N^*(X;\Bbb Fp) ≅ H ^*(XS1;\Bbb Fp) identifies theses Stenrood operations with those defined on the cohomology of the free loop space with coefficients in \Bbb Fp. The other goal of this paper is to describe a theoritic model which allows to do some computations.