Homotopy groups of highly connected Poincare Duality complexes
Homotopy groups of highly connected Poincare Duality complexes
Methods are developed to relate the action of a principal fibration to relative Whitehead products in order to determine the homotopy type of certain spaces. The methods are applied to thoroughly analyze the homotopy type of the based loops on certain cell attachments. Key examples are (n − 1)-connected Poincaré Duality complexes of dimension 2n or 2n + 1 with minor cohomological conditions.
principal fibration, Whitehead product, loop space decomposition, Poincare Duality complex, Principal fibration, Poincaré duality complex
183-211
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Beben, Piotr D
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
2022
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Beben, Piotr D
a74d3e1f-52e0-4dc6-8f20-9c1628a20d2b
Theriault, Stephen and Beben, Piotr D
(2022)
Homotopy groups of highly connected Poincare Duality complexes.
Documenta Mathematica, 27, .
(doi:10.25537/dm.2022v27.183-211).
Abstract
Methods are developed to relate the action of a principal fibration to relative Whitehead products in order to determine the homotopy type of certain spaces. The methods are applied to thoroughly analyze the homotopy type of the based loops on certain cell attachments. Key examples are (n − 1)-connected Poincaré Duality complexes of dimension 2n or 2n + 1 with minor cohomological conditions.
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loop highly connected manifold revised2
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Accepted/In Press date: 22 February 2022
Published date: 2022
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© 2022
Keywords:
principal fibration, Whitehead product, loop space decomposition, Poincare Duality complex, Principal fibration, Poincaré duality complex
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Local EPrints ID: 455422
URI: http://eprints.soton.ac.uk/id/eprint/455422
ISSN: 1431-0635
PURE UUID: 3dd1fddf-6fdd-4598-9510-6c8c64c2c6c0
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Date deposited: 21 Mar 2022 17:50
Last modified: 17 Mar 2024 03:30
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Author:
Piotr D Beben
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