Abstract
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For a simply connected closed orientable manifold of dimension
, we
compute its homotopy decomposition after double suspension. This allows us to determine
its
– and
–groups
easily. Moreover, in a special case we refine the decomposition to show the rigidity
property of the manifold after double suspension.
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Keywords
$6$–manifolds, homotopy decomposition, loop spaces,
coformal spaces, homotopy groups, Poincaré duality space,
$K$–groups
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Mathematical Subject Classification
Primary: 55P15, 55P40, 57R19
Secondary: 55N15, 55P10
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Publication
Received: 15 April 2021
Revised: 27 September 2021
Accepted: 30 October 2021
Published: 27 March 2023
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Publishers). Distributed under the Creative Commons
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