Friedman, John L.; Witt, Donald M. Homotopy is not isotopy for homeomorphisms of 3-manifolds. (English) Zbl 0596.57008 Topology 25, 35-44 (1986). It has been conjectured for a long time that there is no homeomorphism of a closed 3-manifold which is homotopic but not isotopic to the identity. The authors give in this paper the first counterexample known to this conjecture. This counterexample occurs for the connected sum of two 3- manifolds obtained as quotients of \(S^ 3\) by certain finite subgroups of SO(4); the homeomorphism considered is a Dehn twist along the sphere of connected sum. Motivated by certain problems in quantum gravity, the authors also determine the group of isotopy classes of homeomorphisms fixing a point (resp. a ball) for 3-manifolds of this type. Reviewer: F.Bonahon Cited in 2 ReviewsCited in 11 Documents MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) 57R52 Isotopy in differential topology 81T20 Quantum field theory on curved space or space-time backgrounds 57R50 Differential topological aspects of diffeomorphisms Keywords:homeomorphism of a closed 3-manifold; homotopic but not isotopic to the identity; connected sum of two 3-manifolds; Dehn twist; quantum gravity; isotopy classes of homeomorphisms PDFBibTeX XMLCite \textit{J. L. Friedman} and \textit{D. M. Witt}, Topology 25, 35--44 (1986; Zbl 0596.57008) Full Text: DOI