Volume 8, issue 1 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The Thurston polytope for four-stranded pretzel links

Joan E Licata

Algebraic & Geometric Topology 8 (2008) 211–243
Abstract

In this paper we use Heegaard Floer link homology to determine the dual Thurston polytope for pretzel links of the form P(2r1 1,2q1,2q2,2r2 + 1),ri,qi +. We apply this result to determine the Thurston norms of spanning surfaces for the individual link components, and we explicitly construct norm-realizing surfaces for the homology classes which are vertices of the Thurston polytope.

Keywords
Thurston norm, pretzel link, Heegaard Floer, Seifert surface
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 53D99, 57R58, 57M25
References
Publication
Received: 4 October 2006
Revised: 16 August 2007
Accepted: 4 December 2007
Published: 12 March 2008
Authors
Joan E Licata
Department of Mathematics
Stanford University
Stanford, CA 94305
USA
http://math.stanford.edu/~jelicata/