THE JONES POLYNOMIAL AND BOUNDARY SLOPES OF ALTERNATING KNOTS-Reference-Cited by-同舟云学术

THE JONES POLYNOMIAL AND BOUNDARY SLOPES OF ALTERNATING KNOTS

Published:2011-10 Issue:10 Volume:20 Page:1345-1354
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

CURTIS CYNTHIA L.¹,TAYLOR SAMUEL J.²

Affiliation:

1. Department of Mathematics and Statistics, The College of New Jersey Ewing, NJ 08628, USA

2. Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA

Abstract

We show for an alternating knot the minimal boundary slope of an essential spanning surface is given by the signature plus twice the minimum degree of the Jones polynomial and the maximal boundary slope of an essential spanning surface is given by the signature plus twice the maximum degree of the Jones polynomial. For alternating Montesinos knots, these are the minimal and maximal boundary slopes.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216511009194

Reference9 articles.

1. On the signature of a link

2. On the boundary curves of incompressible surfaces

3. Boundary slopes for Montesinos knots

4. Incompressible surfaces in 2-bridge knot complements

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1. A characterisation of alternating knot exteriors;Geometry & Topology;2017-05-19

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4. A classification of spanning surfaces for alternating links;Algebraic & Geometric Topology;2013-07-31