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Suspension homotopy of $6$–manifolds

Ruizhi Huang

Algebraic & Geometric Topology 23 (2023) 439–460
Abstract

For a simply connected closed orientable manifold of dimension 6, we compute its homotopy decomposition after double suspension. This allows us to determine its K– and KO–groups easily. Moreover, in a special case we refine the decomposition to show the rigidity property of the manifold after double suspension.

Keywords
$6$–manifolds, homotopy decomposition, loop spaces, coformal spaces, homotopy groups, Poincaré duality space, $K$–groups
Mathematical Subject Classification
Primary: 55P15, 55P40, 57R19
Secondary: 55N15, 55P10
References
Publication
Received: 15 April 2021
Revised: 27 September 2021
Accepted: 30 October 2021
Published: 27 March 2023
Authors
Ruizhi Huang
Institute of Mathematics
Chinese Academy of Sciences
Beijing
China
https://sites.google.com/site/hrzsea/

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