TORSION IN LOOP SPACE HOMOLOGY OF RATIONALLY CONTRACTIBLE SPACES

By Ran Levi

Appeared in Journal of Pure and Applied Algebra 


Let R be a  torsion free principal ideal 
domain. We study the growth of torsion 
in loop space homology of simply-connected 
dgR-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.