On the Knot Floer Homology of Twisted Torus Knots

2013/11/30 by Faramarz Vafaee · 21 citations
Mathematics · #Advanced Combinatorial Mathematics #Floer homology #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot invariant #Knot theory #Subfamily #Torus #math.GT

paper · pdf · doi:10.1093/imrn/rnu130

published in International Mathematics Research Notices 2015(15), 6516-6537 (Oxford University Press) · 17 pages, 12 figures; v2: minor revisions throughout

openalex publication_date 2014/08/21 · arxiv created 2014/09/03 · openalex created_date 2016/06/24 · arxiv updated 2018/01/16 · openalex updated_date 2026/08/05

Abstract

In this paper, we study the knot Floer homology of a subfamily of twisted (p,q) torus knots where q≡±1 (mod p). Specifically, we classify the knots in this subfamily that admit L-space surgeries. To do calculations, we use the fact that these knots are (1,1) knots and, therefore, admit a genus one Heegaard diagram.

Citations

• Holomorphic disks and knot invariants
• Holomorphic disks and three-manifolds invariants: Properties and applications
• On the Heegaard Floer homology of branched double-covers
• An Introduction to Knot Theory