منابع مشابه
The Thomified Eilenberg-Moore spectral sequence
where Xs+1 is the fiber of gs. We get an exact couple of homotopy groups and a spectral sequence with E 1 = πt−s(Ks) and dr : E s,t r → Es+r,t+r−1 r . This spectral sequence converges to π∗(X) (where X = X0) if the homotopy inverse limit lim←Xs is contractible and certain lim 1 groups vanish. When X is connective, it is a first quadrant spectral sequence. For more background, see [Rav86]. In th...
متن کاملWeights in cohomology and the Eilenberg-Moore spectral sequence
We show that in the category of complex algebraic varieties, the Eilenberg–Moore spectral sequence can be endowed with a weight filtration. This implies that it degenerates if all spaces involved have pure cohomology. As application, we compute the rational cohomology of an algebraic G-variety X (G being a connected algebraic group) in terms of its equivariant cohomology provided that H∗ G(X) i...
متن کاملA 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...
متن کاملA Torsion - Free Milnor - Moore Theorem Jonathan
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, a...
متن کاملOn the Construction of the Eilenberg- Moore Spectral Sequence
where H*( ; k) denotes cohomology with coefficients in the field k. This spectral sequence has proved to be a powerful tool for dealing with numerous problems in algebraic topology [3], [16], [17]. The constructions of [ó] (also [16]), are entirely algebraic in nature and have left open several rather important points, among them the relation between the spectral sequence and the Steenrod algeb...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2002
ISSN: 1370-1444
DOI: 10.36045/bbms/1102715104