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Obstructions to the section problem in fibre bundles

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Abstract

For a Serre fibration with a fibre of theK(π, n)'s product type, obstructions to the section problem in each degree are defined by means of the Hirsch complex of fibration. This allows us to give the homotopy classification of sections (maps) as well as other applications. In particular, forG-bundles, these obstructions are related to theA ∞-module structure on the homology of the fibre and, consequently, some results in the fixed point theory are obtained.

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Authors and Affiliations

  1. Mathematical Institute of the, Georgian Academy of Sciences, Z. Rukhadze Str. 1, 380093, Tbilisi, Republic of Georgia

    Samson Saneblidze

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  1. Samson Saneblidze
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Partially supported by the Forschungsprojekt Topologie und nichtkommutative Geometrie der Universität Heidelberg

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Saneblidze, S. Obstructions to the section problem in fibre bundles. Manuscripta Math 81, 95–111 (1993). https://doi.org/10.1007/BF02567847

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  • DOI: https://doi.org/10.1007/BF02567847

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