2001/09/20 by Bitjong Ndombol, Ndombol, Bitjong, Jean‐Claude Thomas +2
Mathematics · #54C35 #55S20 #57T30 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AG #math.AT #math.KT #msc:54C35 #msc:55S20 #msc:57T30
paper · pdf · doi:10.48550/arxiv.math/0109145
21 pages, to appear in Topology
arxiv created 2001/09/20 · openalex publication_date 2001/09/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Let X be a simply connected space and \Bbb K be any field. The normalized singular cochains N^*(X; \Bbb K) admit a natural strongly homotopy commutative algebra structure, which induces a natural product on the Hochschild homology HH_* N^*X of the space X. We prove that, endowed with this product, HH_*N^*X is isomorphic to the cohomology algebra of the free loop space of X with coefficients in \Bbb K. We also show how to construct a simpler Hochschild complex which allows direct computation.