Algebraic & Geometric Topology

The Thurston polytope for four-stranded pretzel links

Joan Licata

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Abstract

In this paper we use Heegaard Floer link homology to determine the dual Thurston polytope for pretzel links of the form P(2r11,2q1,2q2,2r2+1),ri,qi+. 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.

Article information

Source
Algebr. Geom. Topol., Volume 8, Number 1 (2008), 211-243.

Dates
Received: 4 October 2006
Revised: 16 August 2007
Accepted: 4 December 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796812

Digital Object Identifier
doi:10.2140/agt.2008.8.211

Mathematical Reviews number (MathSciNet)
MR2443228

Zentralblatt MATH identifier
1146.57021

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 53D99: None of the above, but in this section 57R58: Floer homology 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
Thurston norm pretzel link Heegaard Floer Seifert surface

Citation

Licata, Joan. The Thurston polytope for four-stranded pretzel links. Algebr. Geom. Topol. 8 (2008), no. 1, 211--243. doi:10.2140/agt.2008.8.211. https://projecteuclid.org/euclid.agt/1513796812


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