Boundary slopes (nearly) bound cyclic slopes

Mattman, Thomas W

doi:10.2140/agt.2005.5.741

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Boundary slopes (nearly) bound cyclic slopes

Thomas W Mattman

Algebraic & Geometric Topology 5 (2005) 741–750

DOI: 10.2140/agt.2005.5.741

arXiv: math.GT/0407025

Abstract

Let $r_{m}$ and $r_{M}$ be the least and greatest finite boundary slopes of a hyperbolic knot $K$ in $S^{3}$ . We show that any cyclic surgery slopes of $K$ must lie in the interval $(r_{m} - 1 ∕ 2, r_{M} + 1 ∕ 2)$ .

Keywords

Dehn surgery, character variety, exceptional surgery, boundary slope

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M27

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Publication

Received: 16 November 2004

Accepted: 6 March 2005

Published: 23 July 2005

Authors

Thomas W Mattman
Department of Mathematics and Statistics California State University Chico Chico CA 95929-0525 USA

Volume 5, issue 2 (2005)