Exotic convergence of the Eilenberg-Moore spectral sequence
نویسندگان
چکیده
منابع مشابه
Exotic Convergence of the Eilenberg - Moore Spectral Sequence
Let p:E B be a fibration over a connected space B with fiber F. The Eilenberg-Moore spectral sequence of p is a second quadrant spectral sequence which tries and sometimes fails to converge strongly to the homology of F (see 1-53). The purpose of this paper is to determine what the spectral sequence does converge to. An abstract answer (Theorem 1.1) is that the spectral sequence almost always c...
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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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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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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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We prove that the Morava-K-theory-based Eilenberg-Moore spectral sequence has good convergence properties whenever the base space is a p-local finite Postnikov system with vanishing (n + 1)st homotopy group.
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1975
ISSN: 0019-2082
DOI: 10.1215/ijm/1256050669