Suspension homotopy of 6–manifolds

Huang, Ruizhi

doi:10.2140/agt.2023.23.439

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Suspension homotopy of $6$–manifolds

Ruizhi Huang

Algebraic & Geometric Topology 23 (2023) 439–460

DOI: 10.2140/agt.2023.23.439

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 $K O$ –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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Volume 23, issue 1 (2023)