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Lusternik-Schnirelmann category: A geometric approach. (English) Zbl 0639.55002
Geometric and algebraic topology, Banach Cent. Publ. 18, 117-129 (1986).
[For the entire collection see Zbl 0626.00024.]
This is an interesting survey on the aspects of geometric topology in the compact PL case of Lyusternik-Shnirel’man category. The author discusses the relations between the notions of category, geometric category, simple category, and strong category for polyhedra. He presents the Bernstein- Hilton example [cf. Ill. J. Math. 4, 437-451 (1960; Zbl 0113.383)] and he reproduces his simplification [reviewed above (see Zbl 0639.55001)] of Singhof’s theorem that $$cat(P\times S^ r)=cat P+1$$ for every compact connected polyhedron and every $$r\geq 1$$.
Reviewer: Ch.Fenske

##### MSC:
 55M30 Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects) 57Q99 PL-topology