Lusternik-Schnirelmann category and systolic category of low-dimensional manifolds
Lusternik-Schnirelmann category and systolic category of low-dimensional manifolds
We show that the geometry of a Riemannian manifold (M, 𝒢) is sensitive to the apparently purely homotopy-theoretic invariant of M known as the Lusternik-Schnirelmann category, denoted catLS(M). Here we introduce a Riemannian analogue of catLS(M), called the systolic category of M. It is denoted catsys(M) and defined in terms …