Homotopy commutativity and the Moore spectral sequence
نویسندگان
چکیده
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...
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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...
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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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LET p : E-t B be a fibration of pointed spaces with fiber F. Let A be any abelian group, and suppose that the base B is connected. Our main result is: THEOREM. The mod A Eilenberg-Moore spectral sequence of p cotverges strongly to H,(F, A) ifand oni,v if z,(B) acts nilpotently on H,(F, A) for each i 2 0. This statement has to be explained. First of all, the theorem refers to the general " Eilen...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1965
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1965.15.65