Loop homotopy of $6$-manifolds over $4$-manifolds
Algebraic Topology
2023-08-02 v2 Geometric Topology
Abstract
Let be the -manifold as the total space of the sphere bundle of a rank vector bundle over a simply connected closed -manifold. We show that after looping is homotopy equivalent to a product of loops on spheres in general. This particularly implies the cohomology rigidity property of after looping. Furthermore, passing to the rational homotopy, we show that such is Koszul in the sense of Berglund.
Keywords
Cite
@article{arxiv.2105.03881,
title = {Loop homotopy of $6$-manifolds over $4$-manifolds},
author = {Ruizhi Huang},
journal= {arXiv preprint arXiv:2105.03881},
year = {2023}
}
Comments
16 pages; correct the proof of Theorem 1.1