Cohomological estimates for $\cat(X,ξ)$

Abstract

This paper studies the homotopy invariant $\cat(X,ξ)$ introduced in \cite{farbe2}. Given a finite cell-complex $X$, we study the function $ξ\mapsto \cat(X,ξ)$ where $\xi$ varies in the cohomology space $H^1(X;\mathbb{R})$. Note that $\cat(X,ξ)$ turns into the classical Lusternik - Schnirelmann category $\cat(X)$ in the case $\xi =0$. Interest in $\cat(X,ξ)$ is based on its applications in dynamics where it enters estimates of complexity of the chain recurrent set of a flow admitting Lyapunov closed 1-forms.

Cited by in corpus (2)

• Closed 1-Forms in Topology and Geometric Group Theory
• On the relative Lusternik-Schnirelmann category with respect to a closed 1-form