Vol. 71, No. 2, 1977

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An unexpected surgery construction of a lens space

James Bailey and Dale Rolfsen

Vol. 71 (1977), No. 2, 295–298
Abstract

A useful method of constructing-3-dimensional manifolds is to remove the interior of a tubular neighbourhood V S3 of a knot K in the 3-sphere and sew it back differently, via a homeomorphism h : ∂V ∂V . This surgery construction, due to M. Dehn, yields the manifold

                 ⋃
M  3 = (S3 − int V ) V,
h

where x ∂V V is identified with h(x) ∂V S3 int V . For example surgery along a trivial knot yields, for various choices of h, exactly the class of lens spaces L(p,q), including the extreme cases L(1,0)S3 and L(0,1)S2 × S1.

Mathematical Subject Classification
Primary: 57A10, 57A10
Secondary: 55A25
Milestones
Received: 9 April 1975
Revised: 4 May 1976
Published: 1 August 1977
Authors
James Bailey
Dale Rolfsen
Mathematics Department
University of British Columbia
1984 Mathematics Road
Vancouver BC V6T 1Z2
Canada
http://www.math.ubc.ca/~rolfsen/