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Summer 2015 Minimal genus of links and fibering of canonical surfaces
A. Stoimenow
Illinois J. Math. 59(2): 399-448 (Summer 2015). DOI: 10.1215/ijm/1462450708


This paper contains some further applications of the study of knot diagrams by genus. Introducing a procedure of regularization for knot generators, and using invariants derived from the Jones polynomial (degrees, congruences, and the Fiedler–Polyak–Viro Gauß diagram formulas for its Vassiliev invariants), we examine the existence of genus-minimizing diagrams for almost alternating and almost positive knots. In particular, we examine the existence of such knots such that either all or none of their almost alternating/positive diagrams have the minimal genus property. We prove that the genus of almost positive non-split links is determined by the Alexander polynomial.


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A. Stoimenow. "Minimal genus of links and fibering of canonical surfaces." Illinois J. Math. 59 (2) 399 - 448, Summer 2015.


Received: 9 August 2015; Revised: 19 January 2016; Published: Summer 2015
First available in Project Euclid: 5 May 2016

zbMATH: 1342.57011
MathSciNet: MR3499519
Digital Object Identifier: 10.1215/ijm/1462450708

Primary: 57M25
Secondary: 53D10, 57M15, 57N10

Rights: Copyright © 2015 University of Illinois at Urbana-Champaign


Vol.59 • No. 2 • Summer 2015
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