The Thurston polytope for four-stranded pretzel links

Abstract

In this paper we use Heegaard Floer link homology to determine the dual Thurston polytope for pretzel links of the form $P\left(-2r_1-1,2q_1,-2q_2,2r_2+1\right),r_i,q_i\in {\mathbb{Z}}^{+}$. 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.