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The Thurston polytope for four-stranded pretzel links

Joan Licata

Algebraic & Geometric Topology 8 (2008) 211–243

DOI: 10.2140/agt.2008.8.211
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 in Z+. 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

Primary: 57M27

Secondary: 53D99, 57M25, 57R58
References
Publication

Received: 4 October 2006
Revised: 16 August 2007
Accepted: 4 December 2007
Published: 12 March 2008
Authors
Joan Licata
Department of Mathematics
Stanford University
Stanford, CA 94305
USA
http://math.stanford.edu/~jelicata/