English

The Lusternik-Schnirelmann category of connected sum

Algebraic Topology 2019-10-01 v1 Geometric Topology

Abstract

We use the Berstein-Hilton invariant to prove the formula \cat(M1M2)=max{\catM1,\catM2}\cat(M_1\sharp M_2)=\max\{\cat M_1, \cat M_2\} for the Lustrnik-Schnirelmann category of the connected sum of closed manifolds M1M_1 and M2M_2.

Keywords

Cite

@article{arxiv.1909.12976,
  title  = {The Lusternik-Schnirelmann category of connected sum},
  author = {Alexander Dranishnikov and Rustam Sadykov},
  journal= {arXiv preprint arXiv:1909.12976},
  year   = {2019}
}