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The rational homotopy type of homotopy fibrations over connected sums

The rational homotopy type of homotopy fibrations over connected sums
The rational homotopy type of homotopy fibrations over connected sums
We provide a simple condition on rational cohomology for the total space of a pullback fibration over a connected sum to have the rational homotopy type of a connected sum after looping. This takes inspiration from a recent work of Jeffrey and Selick, in which they study pullback fibrations of this type but under stronger hypotheses compared to our result.
Poincaré duality, connected sums, fibration, loop spaces, rational homotopy theory
1464-3839
133-142
Chenery, Sebastian David
b30ec616-4e86-4290-8978-d42b336ac2f8
Chenery, Sebastian David
b30ec616-4e86-4290-8978-d42b336ac2f8

Chenery, Sebastian David (2023) The rational homotopy type of homotopy fibrations over connected sums. Proceedings of the Edinburgh Mathematical Society, 66 (1), 133-142. (doi:10.1017/S001309152300007X).

Record type: Article

Abstract

We provide a simple condition on rational cohomology for the total space of a pullback fibration over a connected sum to have the rational homotopy type of a connected sum after looping. This takes inspiration from a recent work of Jeffrey and Selick, in which they study pullback fibrations of this type but under stronger hypotheses compared to our result.

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Fibrations_Over_Connected_Sums_v2_2 - Accepted Manuscript
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Accepted/In Press date: 26 January 2023
Published date: 3 April 2023
Additional Information: Publisher Copyright: © The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.
Keywords: Poincaré duality, connected sums, fibration, loop spaces, rational homotopy theory

Identifiers

Local EPrints ID: 477208
URI: http://eprints.soton.ac.uk/id/eprint/477208
ISSN: 1464-3839
PURE UUID: 3562e9db-3c91-41d7-9cd9-effc4ce0624a

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Date deposited: 01 Jun 2023 16:39
Last modified: 06 Jun 2024 04:09

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