Transactions of the American Mathematical Society

Author(s): Yves Félix; Stephen Halperin; Jean-Claude Thomas
Journal: Trans. Amer. Math. Soc. 353 (2001), 3803-3831.
MSC (2000): Primary 57T25, 55R20, 57T05
Posted: April 24, 2001
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In a fibration $\Omega F \overset{\Omega j}{\rightarrow} \Omega X \overset{\Omega \pi}{\rightarrow}\Omega B$ we show that finiteness conditions on

force the homology Serre spectral sequence with $\mathbb{F} _p$ -coefficients to collapse at some finite term. This in particular implies that as graded vector spaces, $H_*(\Omega X)$ is ``almost'' isomorphic to $H_*(\Omega B)\otimes H_*(\Omega F)$ . One consequence is the conclusion that

is elliptic if and only if

and

are.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 57T25, 55R20, 57T05

Yves Félix
Affiliation: Institut de Mathématiques, Université de Louvain-la-Neuve, B-1348 Louvain-la- Neuve, Belgium

Stephen Halperin
Affiliation: College of Computer, Mathematical and Physical Sciences, University of Maryland, College Park, Maryland 20742-3281

Jean-Claude Thomas
Affiliation: Faculté des Sciences, Université d'Angers, 49045 bd Lavoisier, Angers, France

DOI: 10.1090/S0002-9947-01-02801-X
PII: S 0002-9947(01)02801-X
Keywords: Multiplicative fibration, loop space, Hopf algebra, Serre spectral sequences, elliptic space
Received by editor(s): January 30, 1998
Posted: April 24, 2001
Additional Notes: Research of the second author was partially supported by an NSERC operating grant. Research of the first and third authors was partially supported by UMR-6093 au CNRS
This work was also partially supported by a NATO travel grant held by all three authors.
Copyright of article: Copyright 2001, American Mathematical Society

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