Serre's contribution to the development of algebraic topology

    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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