Vol. 74, No. 2, 1978

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Involutions of Seifert fiber spaces

Jeffrey L. Tollefson

Vol. 74 (1978), No. 2, 519–529

A Seifert fiber space M is a compact 3-manifold which decomposes into a collection of disjoint simple closed curves, called fibers, such that each fiber has a tubular neighborhood which consists of fibers and is a “standard fibered solid torus.” We consider the question, given a PL involution h of M, can the fiber structure be chosen in such a way that h will be fiber-preserving? We give an affirmative answer for the case when M is orientable, irreducible, and either ∂Mor M contains an incompressible fibered torus.

Mathematical Subject Classification
Primary: 57A10, 57A10
Received: 9 November 1976
Published: 1 February 1978
Jeffrey L. Tollefson