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Cosmetic surgery on knots

Steven A Bleiler, Craig D Hodgson and Jeffrey R Weeks

Geometry & Topology Monographs 2 (1999) 23–34

DOI: 10.2140/gtm.1999.2.23

arXiv: math.GT/9911247

Abstract
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This paper concerns the Dehn surgery construction, especially those Dehn surgeries leaving the manifold unchanged. In particular, we describe an oriented 1–cusped hyperbolic 3–manifold X with a pair of slopes r1, r2 such that the Dehn filled manifolds X(r1), X(r2) are oppositely oriented copies of the lens space L(49,18), and there is no homeomorphism h of X such that h(r1) = h(r2).

Keywords

Dehn surgery, Dehn filling, hyperbolic knots

Mathematical Subject Classification

Primary: 57N10

Secondary: 57M25, 57M50

References
Publication

Received: 27 January 1999
Revised: 15 June 1999
Published: 17 November 1999

Authors
Steven A Bleiler
Department of Mathematics
Portland State University
Portland OR 97207-0751
USA
Craig D Hodgson
Department of Mathematics
University of Melbourne
Parkville
Victoria 3052
Australia
Jeffrey R Weeks
15 Farmer Street
Canton
New York
USA