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A Torsion-Free Milnor-Moore Theorem | | Jonathan A. Scott
; | | Date: |
30 Mar 2001 | | Subject: | Algebraic Topology MSC-class: 55P35 | math.AT | | Abstract: | Let Omega X be the space of Moore loops on a finite, q-connected, n-dimensional CW complex X, and let R be a subring of Q containing 1/2. Let p(R) be the least non-invertible prime in R. For a graded R-module M of finite type, let FM = M / Torsion M. We show that the inclusion of the sub-Lie 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 finitely-generated R-algebra. | | Source: | arXiv, math.AT/0103223 | | Services: | Forum | Review | PDF | Favorites | |
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