The Lusternik–Schnirelmann category of a connected sum
Volume 251 / 2020
Fundamenta Mathematicae 251 (2020), 317-328
MSC: Primary 55M30; Secondary 57R19.
DOI: 10.4064/fm792-1-2020
Published online: 5 June 2020
Abstract
We use the Berstein–Hilton invariant to prove the formula $\operatorname{cat} (M\mathbin {\sharp } N)=\max \{\operatorname{cat} M, \operatorname{cat} N\}$ for the Lusternik–Schnirelmann category of the connected sum of closed manifolds $M$ and $N$.
