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

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.

MSC:

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