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 . 2r 1 1; 2q 1 ; 2q 2 ; 2r 2 C 1/; r i ; q i 2 Z C . 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. 57M27; 53D99, 57R58, 57M25

Thurston norms of tunnel number-one manifolds

“…For example, it would be interesting if these manifolds were all link complements that had a uniform construction. In [7], Licata used Heegaard Floer homology to compute M π for all two-component, four-strand pretzel links, and the unit balls are shaped similarly to the polytopes we construct. On the other hand, all of Licata's examples have 8 vertices, so cannot match our examples.…”