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Minimal genus and fibering of canonical surfaces via disk decomposition

Part of: Topological manifolds Low-dimensional topology Symplectic geometry, contact geometry

Published online by Cambridge University Press:  01 May 2014

A. Stoimenow
A. Stoimenow*
Affiliation:
Gwangju Institute of Science and Technology, School of General Studies, GIST College, 123 Cheomdan-gwagiro, 1 Oryong-dong, Buk-gu, Gwangju 500-712, Korea email stoimeno@stoimenov.nethttp://stoimenov.net/stoimeno/homepage/

Abstract

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This paper contains some applications of the description of knot diagrams by genus, and Gabai’s methods of disk decomposition. We show that there exists no genus one knot of canonical genus 2, and that canonical genus 2 fiber surfaces realize almost every Alexander polynomial only finitely many times (partially confirming a conjecture of Neuwirth).

MSC classification

Secondary: 57M25: Knots and links in $S^3$ 57N10: Topology of general $3$-manifolds 53D10: Contact manifolds, general 57M15: Relations with graph theory
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Issue 1 , 2014 , pp. 77 - 108
Copyright
© The Author 2014 

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