McCullough, Darryl 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 Cited in 2 ReviewsCited in 8 Documents 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 Keywords:reducible 3-manifolds; homotopy equivalences; homeomorphisms; mapping class groups; fundamental group of the space of homeomorphisms; aspherical manifolds Citations:Zbl 0626.00024 PDFBibTeX XML