scholarly journals Knots which admit a surgery with simple knot Floer homology groups

2011 ◽  
Vol 11 (3) ◽  
pp. 1243-1256 ◽  
Author(s):  
Eaman Eftekhary
Keyword(s):  
Floer Homology ◽  
Homology Groups ◽  
Knot Floer Homology

scholarly journals CONSTRUCTING DOUBLY-POINTED HEEGAARD DIAGRAMS COMPATIBLE WITH (1,1) KNOTS

2013 ◽  
Vol 22 (11) ◽  
pp. 1350071
Author(s):  
PHILIP ORDING
Keyword(s):  
Normal Form ◽  
Floer Homology ◽  
Solid Torus ◽  
Heegaard Splitting ◽  
Heegaard Diagrams ◽  
Homology Groups ◽  
Knot Floer Homology ◽  
Heegaard Diagram ◽  
Train Tracks

A (1,1) knot K in a 3-manifold M is a knot that intersects each solid torus of a genus 1 Heegaard splitting of M in a single trivial arc. Choi and Ko developed a parametrization of this family of knots by a four-tuple of integers, which they call Schubert's normal form. This paper presents an algorithm for constructing a genus 1 doubly-pointed Heegaard diagram compatible with K, given a Schubert's normal form for K. The construction, coupled with results of Ozsváth and Szabó, provides a practical way to compute knot Floer homology groups for (1,1) knots. The construction uses train tracks, and its method is inspired by the work of Goda, Matsuda, and Morifuji.

scholarly journals SYMMETRIES AND ADJUNCTION INEQUALITIES FOR KNOT FLOER HOMOLOGY

2012 ◽  
Vol 21 (10) ◽  
pp. 1250104 ◽  
Author(s):  
BIJAN SAHAMIE
Keyword(s):  
Floer Homology ◽  
Homology Groups ◽  
Knot Floer Homology

We derive symmetries and adjunction inequalities of the knot Floer homology groups which appear to be especially interesting for homologically essential knots. Furthermore, we obtain an adjunction inequality for cobordism maps in knot Floer homologies. We demonstrate the adjunction inequalities and symmetries in explicit calculations which recover some of the main results from [E. Eftekhary, Longitude Floer homology and the Whitehead double, Algebr. Geom. Topol. 5 (2005) 1389–1418] on longitude Floer homology and also give rise to vanishing results on knot Floer homologies.

scholarly journals COMBINATORIAL KNOT FLOER HOMOLOGY AND DOUBLE BRANCHED COVERS

2013 ◽  
Vol 22 (06) ◽  
pp. 1350014
Author(s):  
FATEMEH DOUROUDIAN
Keyword(s):  
Floer Homology ◽  
Combinatorial Proof ◽  
Branched Covers ◽  
Knot Floer Homology ◽  
Branched Cover ◽  
Heegaard Diagram

Using a Heegaard diagram for the pullback of a knot K ⊂ S3 in its double branched cover Σ2(K), we give a combinatorial proof for the invariance of the associated knot Floer homology over ℤ.

scholarly journals An introduction to knot Floer homology and curved bordered algebras

2020 ◽  
Vol 80 (2) ◽  
pp. 211-236
Author(s):  
Antonio Alfieri ◽  
Jackson Van Dyke
Keyword(s):  
Floer Homology ◽  
Knot Floer Homology

scholarly journals Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology

2008 ◽  
Vol 2008 ◽  
Author(s):  
Kenneth L. Baker ◽  
J. Elisenda Grigsby ◽  
Matthew Hedden
Keyword(s):  
Floer Homology ◽  
Lens Spaces ◽  
Knot Floer Homology ◽  
Grid Diagrams

scholarly journals A combinatorial spanning tree model for knot Floer homology

2012 ◽  
Vol 231 (3-4) ◽  
pp. 1886-1939 ◽  
Author(s):  
John A. Baldwin ◽  
Adam Simon Levine
Keyword(s):  
Spanning Tree ◽  
Floer Homology ◽  
Tree Model ◽  
Knot Floer Homology

scholarly journals A cube of resolutions for knot Floer homology

2009 ◽  
Vol 2 (4) ◽  
pp. 865-910 ◽  
Author(s):  
Peter Ozsváth ◽  
Zoltán Szabó
Keyword(s):  
Floer Homology ◽  
Knot Floer Homology
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