#### Volume 8, issue 1 (2008)

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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 $P\left(-2{r}_{1}-1,2{q}_{1},-2{q}_{2},2{r}_{2}+1\right),{r}_{i},{q}_{i}\in {ℤ}^{+}$. 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