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Mappings or reducible 3-manifolds. (English) Zbl 0637.57009

Geometric and algebraic topology, Banach Cent. Publ. 18, 61-76 (1986).
[For the entire collection see Zbl 0626.00024.]
The author gives a brief survey of results on reducible 3-manifolds, holding each next to the corresponding result for irreducible 3- manifolds. The areas covered include homotopy equivalences, homeomorphisms, mapping class groups, and the fundamental group of the space of homeomorphisms. A proof is given that the latter is not finitely generated if the manifold in question is the sum of 3 or more closed aspherical manifolds.
Reviewer: L.Neuwirth

MSC:

57N10 Topology of general \(3\)-manifolds (MSC2010)
57M05 Fundamental group, presentations, free differential calculus
55P10 Homotopy equivalences in algebraic topology
57R50 Differential topological aspects of diffeomorphisms

Citations:

Zbl 0626.00024