Title

Serre'S Contribution To The Development Of Algebraic Topology

Keywords

Classes of abelian groups; Homology groups; Homotopy groups; Serre; Spectral sequence

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.

Publication Date

1-1-2004

Publication Title

Expositiones Mathematicae

Volume

22

Issue

4

Number of Pages

375-383

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0723-0869(04)80015-X

Socpus ID

4043128127 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/4043128127

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