The Thurston polytope for four-stranded pretzel links

Licata, Joan

doi:10.2140/agt.2008.8.211

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The Thurston polytope for four-stranded pretzel links

Joan E 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 $P (- 2 r_{1} - 1, 2 q_{1}, - 2 q_{2}, 2 r_{2} + 1), r_{i}, q_{i} \in ℤ^{+}$ . 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 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/

Volume 8, issue 1 (2008)