The Serre spectral sequence of a multiplicative fibration
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- by Yves Félix, Stephen Halperin and Jean-Claude Thomas
- Trans. Amer. Math. Soc. 353 (2001), 3803-3831
- DOI: https://doi.org/10.1090/S0002-9947-01-02801-X
- Published electronically: April 24, 2001
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Abstract:
In a fibration $\Omega F \overset {\Omega j}{\rightarrow } \Omega X \overset {\Omega \pi }{\rightarrow }\Omega B$ we show that finiteness conditions on $F$ 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 $X$ is elliptic if and only if $B$ and $F$ are.References
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Bibliographic Information
- 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
- Received by editor(s): January 30, 1998
- Published electronically: 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 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 3803-3831
- MSC (2000): Primary 57T25, 55R20, 57T05
- DOI: https://doi.org/10.1090/S0002-9947-01-02801-X
- MathSciNet review: 1837260