Homotopy of manifolds stabilized by projective spaces
Algebraic Topology
2023-08-03 v2 Geometric Topology
Abstract
We study the homotopy of the connected sum of a manifold with a projective space, viewed as a typical way to stabilize manifolds. In particular, we show a loop homotopy decomposition of a manifold after stabilization by a projective space, and provide concrete examples. To do this, we trace the effect in homotopy theory of surgery on certain product manifolds by showing a loop homotopy decomposition after localization away from the order of the image of the classical -homomorphism.
Cite
@article{arxiv.2204.04368,
title = {Homotopy of manifolds stabilized by projective spaces},
author = {Ruizhi Huang and Stephen Theriault},
journal= {arXiv preprint arXiv:2204.04368},
year = {2023}
}
Comments
Accepted version in Journal of Topology