Complement theorems in shape theory. II. (English) Zbl 0631.55006

Sher, R. B.

Geometric topology and shape theory, Proc. Conf., Dubrovnik/Yugosl. 1986, Lect. Notes Math. 1283, 212-220 (1987).

[For the entire collection see Zbl 0619.00017.]
[For Part I, cf. Proc. Am. Math. Soc. 91, 123-132 (1984; Zbl 0553.57006).]
This paper is an exposition of the current status of mathematical research in four areas: (a) Shape concordance and complements; (b) Complement theorems in the fiber shape catgory; (c) Uniform structures on complements; (d) Shape theory and the stable homotopy of complements. A final section contains three open questions on shape theory.

Reviewer: D.G.Wright

MSC:

55P55	Shape theory
57N25	Shapes (aspects of topological manifolds)
54C56	Shape theory in general topology
55Q05	Homotopy groups, general; sets of homotopy classes

Keywords:

Shape concordance; Complement theorems in the fiber shape catgory; Uniform structures on complements; stable homotopy of complements