Applications of Lusternik-Schnirelmann category and its generalizations. (English) Zbl 1330.55002

Oprea, John

J. Geom. Symmetry Phys. 36, 59-97 (2014).

The author describes diverse applications of the category of a topological space (in the sense of Lusternik and Schnirelmann) to various areas of mathematics. For example: Brouwer fixed point theorem, Morse theory, Symplectic geometry, Nonnegative Ricci curvature, Smale topological complexity, etc.

Reviewer: Jean Claude Thomas (Angers)

MSC:

55-02	Research exposition (monographs, survey articles) pertaining to algebraic topology
55M30	Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects)
55P62	Rational homotopy theory
55P50	String topology

Keywords:

Lusternik-Schnirelmann category; fixed point theorem; topological complexity