Geometry & Topology Monographs 2 (1999), Proceedings of the Kirbyfest, paper no. 2, pages 23-34.

Cosmetic Surgery on Knots

Steven A Bleiler, Craig D Hodgson, Jeffrey R Weeks

Abstract. 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 r_1, r_2 such that the Dehn filled manifolds X(r_1), X(r_2) are oppositely oriented copies of the lens space L(49,18), and there is no homeomorphism h of X such that h(r_1)=h(r_2).

Keywords. Dehn surgery, Dehn filling, hyperbolic knots

AMS subject classification. Primary: 57N10. Secondary: 57M25, 57M50.

E-print: arXiv:math.GT/9911247

Submitted: 27 January 1999. (Revised: 15 June 1999.) Published: 17 November 1999.

Notes on file formats

Steven A Bleiler, Craig D Hodgson, Jeffrey R Weeks

Department of Mathematics, Portland State University Portland, OR 97207-0751, USA

Department of Mathematics, University of Melbourne Parkville, Victoria 3052, Australia

15 Farmer Street, Canton, NY, USA

Email: steve@mth.pdx.edu, cdh@ms.unimelb.edu.au, weeks@northnet.org


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