An upper bound for the Lusternik-Schnirelmann category of the symplectic group

TL;DR

This paper establishes an upper bound for the Lusternik-Schnirelmann category of the symplectic group Sp(n), using critical level analysis of a height function to derive the bound.

Contribution

The paper provides a new upper bound for the LS category of Sp(n), advancing understanding of its topological complexity.

Findings

LS category of Sp(n) is at most (n+1 choose 2)

Critical levels of a height function determine the bound

Method can be applied to similar topological groups

Abstract

We prove that the LS category of the symplectic group $Sp(n)$ is bounded above by $\binom{n+1}{2}$. This is achieved by computing the number of critical levels of a height function.