Aspects of Lusternik-Schnirelmann category (Q2825589)

This paper provides a short and self-contained survey of the theory of Lusternik-Schnirelmann category and related topics. The article arose from a talk given by the author at the Varna conference [Proceedings of the 16th international conference on geometry, integrability and quantization, Sofia: Avangard Prima. 13--35 (2015; Zbl 1317.00020)]. The Lusternik-Schnirelmann category is a numerical invariant in algebraic topology, associated to each topological space. The text is based on recent research results obtained by different authors and contains elegant proofs.NEWLINENEWLINE Further, the author introduces a new invariant, called the universal cover category, in order to provide a new upper bound for Lusternik-Schnirelmann category of a normal space.NEWLINENEWLINEFor the entire collection see [Zbl 1317.00020].