Ran Levi
Torsion in Loop Space Homology of Rationally Contractible Spaces
Abstract
Let $\R$ be a torsion free principal ideal domain. We study the growth of torsion in loop space homology of simply-connected $\dg\R$-coalgebras $C$, whose homology admits an exponent $r$ in $R$. Here by loop space homology we mean the homology of the loop algebra construction on $C$. We compute a bound on the growth of torsion in such objects and show that in general this bound is best possible. Our methods are applied to certain simply-connected spaces associated with classifying spaces of finite groups, where we are able to deduce the existence of global exponents in loop space homology.