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SU(2)-bundles over highly connected 8-manifolds

Part of: Fiber spaces and bundles Homotopy theory Differential topology Generalized manifolds

Published online by Cambridge University Press:  18 February 2025

Samik Basu ,
Aloke Kr Ghosh  and
Subhankar Sau Open the ORCID record for Subhankar Sau [Opens in a new window]
Samik Basu*
Affiliation:
Stat Math Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata, 700108, India (samik.basu2@gmail.com) (corresponding author)
Aloke Kr Ghosh
Affiliation:
Stat Math Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India (alokekrghosh005@gmail.com)
Subhankar Sau
Affiliation:
Stat Math Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India (subhankarsau18@gmail.com)
*
*Corresponding author.
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Abstract

In this paper, we analyse the possible homotopy types of the total space of a principal SU(2)-bundle over a 3-connected 8-dimensional Poincaré duality complex. Along the way, we also classify the 3-connected 11-dimensional complexes E formed from a wedge of S4’s and S7’s by attaching a 11-cell.

Keywords

loop spacesPoincaré duality complexesprincipal bundlessphere fibrations

MSC classification

Primary: 55R25: Sphere bundles and vector bundles 57P10: Poincaré duality spaces
Secondary: 57R19: Algebraic topology on manifolds 55P35: Loop spaces
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 30
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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