A Torsion - Free Milnor - Moore Theorem Jonathan
نویسنده
چکیده
Let ΩX be the space of Moore loops on a finite, qconnected, n-dimensional CW complex X , and let p be an odd prime. We prove the theorem: If p ≥ n/q, then the Hurewicz homomorphism induces isomorphisms U(Fπ∗(ΩX(p))) = −→ FH∗(ΩX(p)) and UE ∞ π (ΩX) = −→ E∞ H (ΩX) of Hopf algebras, where E ∞ π and E ∞ H are the limit terms of the homotopy and homology Bockstein spectral sequences, respectively, and F(−) indicates quotient by torsion.
منابع مشابه
A Torsion - Free Milnor - Moore Theorem
Let ΩX be the space of Moore loops on a finite, qconnected, n-dimensional CW complex X , and let R ⊂ Q be a subring containing 1/2. Let ρ(R) be the least non-invertible prime in R. For a graded R-module M of finite type, let FM = M/TorsionM . We show that the inclusion P ⊂ FH∗(ΩX ;R) of the sub-Lie algebra of primitive elements induces an isomorphism of Hopf algebras UP ∼ = −→ FH∗(ΩX ;R), provi...
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