The LS-category of the product of lens spaces

Abstract

We reduced Rudyak's conjecture that a degree one map between closed manifolds cannot raise the Lusternik-Schnirelmann category to the computation of the category of the product of two lens spaces $L_p^n\times L_q^n$ with relatively prime $p$ and $q$. We have computed $cat(L_p^n\times L_q^n)$ for values of $p,q>n/2$. It turns out that our computation supports the conjecture. For spin manifolds $M$ we establish a criterion for the equality $catM=dimM-1$ which is a K-theoretic refinement of the Katz-Rudyak criterion for $catM=dimM$. We apply it to obtain the inequality $cat(L_p^n\times L_q^n)\le 2n-2$ for all $n$ and odd relatively prime $p$ and $q$.

References in corpus (1)

• On the Berstein-Svarc Theorem in dimension 2

Cited by in corpus (3)

• An upper bound on the LS-category in presence of the fundamental group
• Various Topological Complexities of Small Covers and Real Bott Manifolds
• On some problems related to the Hilbert-Smith conjecture