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

Ruizhi Huang

Algebraic & Geometric Topology 23 (2023) 2369–2388
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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