Loop homotopy of 6–manifolds over 4–manifolds

Huang, Ruizhi

doi:10.2140/agt.2023.23.2369

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Loop homotopy of $6$–manifolds over $4$–manifolds

Ruizhi Huang

Algebraic & Geometric Topology 23 (2023) 2369–2388

DOI: 10.2140/agt.2023.23.2369

Abstract

Let $M$ be the $6$ –manifold $M$ arising as the total space of the sphere bundle of a rank $3$ vector bundle over a simply connected closed $4$ –manifold. We show that, after looping, $M$ is homotopy equivalent to a product of loops on spheres in general. This particularly implies a cohomological rigidity property of $M$ after looping. Furthermore, passing to rational homotopy we show that such an $M$ is Koszul.

Keywords

$6$–manifolds, homotopy decomposition, loop spaces, coformal spaces, homotopy groups

Mathematical Subject Classification

Primary: 55P15, 55P35, 57R19

Secondary: 55P10, 55P40, 55P62

References

Publication

Received: 9 November 2021

Revised: 2 December 2021

Accepted: 19 December 2021

Published: 25 July 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 5 (2023)