A TorsionFree MilnorMoore Theorem
Abstract
Let \Omega X be the space of Moore loops on a finite, qconnected, ndimensional CW complex X, and let R be a subring of Q containing 1/2. Let p(R) be the least noninvertible prime in R. For a graded Rmodule M of finite type, let FM = M / Torsion M. We show that the inclusion of the subLie algebra P of primitive elements of FH_*(\Omega X;R) induces an isomorphism of Hopf algebras UP = FH_*(\Omega X;R), provided p(R) > n/q  1. Furthermore, the Hurewicz homomorphism induces an embedding of F(\pi_*(\Omega X)\otimes R) in P, with torsion cokernel. As a corollary, if X is elliptic, then FH_*(\Omega X;R) is a finitelygenerated Ralgebra.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2001
 arXiv:
 arXiv:math/0103223
 Bibcode:
 2001math......3223S
 Keywords:

 Algebraic Topology;
 55P35
 EPrint:
 12 pages, error corrected, some new ramifications discussed