On the Lusternik-Schnirelmann category of symmetric spaces of classical type

TL;DR

This paper calculates the Lusternik-Schnirelmann category for specific symmetric Riemannian spaces, providing exact topological complexity measures for these classical types.

Contribution

It determines the Lusternik-Schnirelmann category for the symmetric spaces SU(n)/SO(n) and SU(2n)/Sp(n), advancing understanding of their topological properties.

Findings

Lusternik-Schnirelmann category for SU(n)/SO(n) computed

Lusternik-Schnirelmann category for SU(2n)/Sp(n) computed

Provides exact topological invariants for these symmetric spaces

Abstract

We determine the Lusternik-Schnirelmann category of the irreducible, symmetric Riemann spaces SU(n)/SO(n) and SU(2n)/Sp(n) of type AI and AII respectively.