Open AccessOn the Borel cohomology of free loop spaces
Author(s) -
Iver Ottesen
Publication year - 2003
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-14419
Subject(s) - mathematics , cohomology , lambda , loop (graph theory) , omega , space (punctuation) , homomorphism , functor , combinatorics , product (mathematics) , prime (order theory) , loop space , discrete mathematics , pure mathematics , geometry , physics , quantum mechanics , linguistics , philosophy
Let $X$ be a space and let $K = H^*(X; \boldsymbol F_p)$ where $p$ is an odd prime. We construct functors $\overline \Omega$ and $\ell$ which approximate cohomology of the free loop space $\Lambda X$ as follows: There are homomorphisms $\overline \Omega(K) \to H^*(\Lambda X; \boldsymbol F_p)$ and $\ell(K)\to H^*(E\boldsymbol T\times_T\Lambda X;\boldsymbol F_p)$. These are isomorphisms when $X$ is a product of Eilenberg-MacLane spaces of type $K(\boldsymbol F_p,n)$ for $n \geq 1$.