Hodgson, Craig; Rubinstein, J. H. Involutions and isotopies of lens spaces. (English) Zbl 0605.57022 Knot theory and manifolds, Proc. Conf., Vancouver/Can. 1983, Lect. Notes Math. 1144, 60-96 (1985). [For the entire collection see Zbl 0564.00014.] The authors obtain a classification of all involutions of a (3- dimensional) lens space which have 1-dimensional fixed point set. More precisely, they prove that each such involution is conjugate, by a diffeomorphism isotopic to the identity, to an isometry of the spherical metric of the lens space. As a corollary, they determine the group of isotopy classes of diffeomorphisms of each lens space. Another corollary is that a knot in \(S^ 3\) whose double branched covering is a lens space is necessarily a 2-bridge knot. Reviewer: F.Bonahon Cited in 2 ReviewsCited in 31 Documents MSC: 57S25 Groups acting on specific manifolds 57M12 Low-dimensional topology of special (e.g., branched) coverings 57M25 Knots and links in the \(3\)-sphere (MSC2010) 57N10 Topology of general \(3\)-manifolds (MSC2010) Keywords:involutions of lens space; 1-dimensional fixed point set; isometry; 2- bridge knot Citations:Zbl 0564.00014 PDF BibTeX XML OpenURL