Title

Serre's contribution to the development of algebraic topology

Authors

Authors

P. Hilton

Comments

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Abbreviated Journal Title

Expo. Math.

Keywords

spectral sequence; homotopy groups; homology groups; classes of abelian; groups; Serre; Mathematics

Abstract

We describe in detail Serre's application of spectral sequence theory to the study of the relations between the homology of total space, base space and fibre in a Serre fibration and we apply the results to establish that a 1-connected space X has homology groups (in positive dimension) in a Serre class C if and only if its homotopy groups are in C. We include in this paper some personal reflections on the contact the author had with Serre during the decade of the 1950's when Serre's revolutionary work in homotopy theory was completely changing the face of algebraic topology.

Journal Title

Expositiones Mathematicae

Volume

22

Issue/Number

4

Publication Date

1-1-2004

Document Type

Article

Language

English

First Page

375

Last Page

383

WOS Identifier

WOS:000223427400004

ISSN

0723-0869

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