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


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)


Zbl 0564.00014