#### 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

GT home page

## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**