Geodesic
Boundary slopes (nearly) bound cyclic slopes
Mattman, Thomas W1
1Department of Mathematics and Statistics, California State University, Chico, Chico CA 95929-0525, USA
Algebraic and Geometric Topology, Tome 5 (2005) no. 2, pp. 741-750
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Let rm and rM be the least and greatest finite boundary slopes of a hyperbolic knot K in S3. We show that any cyclic surgery slopes of K must lie in the interval (rm − 1∕2,rM + 1∕2).

DOI : 10.2140/agt.2005.5.741
Keywords: Dehn surgery, character variety, exceptional surgery, boundary slope

Mattman, Thomas W  1

1 Department of Mathematics and Statistics, California State University, Chico, Chico CA 95929-0525, USA 
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Mattman, Thomas W. Boundary slopes (nearly) bound cyclic slopes. Algebraic and Geometric Topology, Tome 5 (2005) no. 2, pp. 741-750. doi: 10.2140/agt.2005.5.741

[1] M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Ann. of Math. $(2)$ 125 (1987) 237

[2] M Culler, P B Shalen, Boundary slopes of knots, Comment. Math. Helv. 74 (1999) 530

[3] N M Dunfield, Cyclic surgery, degrees of maps of character curves, and volume rigidity for hyperbolic manifolds, Invent. Math. 136 (1999) 623

[4] M Ishikawa, T W Mattman, K Shimokawa, Exceptional surgery and boundary slopes, Osaka J. Math. 43 (2006) 807

[5] T W Mattman, The Culler–Shalen seminorms of pretzel knots, PhD thesis, McGill University, Montreal (2000)

[6] T W Mattman, The Culler–Shalen seminorms of the $(-3,3,4)$ pretzel knot, from: "Knot Theory – dedicated to Prof. Murasugi (Univ. of Toronto, 1999)" (2000) 212

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