The Serre spectral sequence of a multiplicative fibration期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The Serre spectral sequence of a multiplicative fibration

Authors:	Yves Fé lix Stephen Halperin Jean-Claude Thomas

Institution:	Institut de Mathématiques, Université de Louvain-la-Neuve, B-1348 Louvain-la- Neuve, Belgium Stephen Halperin ; College of Computer, Mathematical and Physical Sciences, University of Maryland, College Park, Maryland 20742-3281 Jean-Claude Thomas ; Faculté des Sciences, Université d'Angers, 49045 bd Lavoisier, Angers, France

Abstract:	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.

Keywords:	Multiplicative fibration loop space Hopf algebra Serre spectral sequences elliptic space

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