English

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 JJ-homomorphism.

Keywords

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