The Lusternik-Schnirelmann category of connected sum

TL;DR

This paper proves a formula for the Lusternik-Schnirelmann category of the connected sum of closed manifolds using the Bernstein-Hilton invariant, showing it equals the maximum of the categories of the summands.

Contribution

It establishes a precise formula for the Lusternik-Schnirelmann category of connected sums of closed manifolds, utilizing the Bernstein-Hilton invariant.

Findings

The LS category of connected sum equals the maximum of individual categories.

The proof employs the Bernstein-Hilton invariant.

The result simplifies computation of LS categories for connected sums.

Abstract

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