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 Rational cobordisms and integral homology

2020 ◽  
Vol 156 (9) ◽  
pp. 1825-1845
Author(s):  
Paolo Aceto ◽  
Daniele Celoria ◽  
JungHwan Park
Keyword(s):  
Homology Group ◽  
Floer Homology ◽  
Lens Spaces ◽  
Integral Homology ◽  
Rational Homology ◽  
Cobordism Class ◽  
Connected Sum ◽  
Knot Floer Homology ◽  
Infinite Rank ◽  
Homology Cobordism

We consider the question of when a rational homology $3$-sphere is rational homology cobordant to a connected sum of lens spaces. We prove that every rational homology cobordism class in the subgroup generated by lens spaces is represented by a unique connected sum of lens spaces whose first homology group injects in the first homology group of any other element in the same class. As a first consequence, we show that several natural maps to the rational homology cobordism group have infinite-rank cokernels. Further consequences include a divisibility condition between the determinants of a connected sum of $2$-bridge knots and any other knot in the same concordance class. Lastly, we use knot Floer homology combined with our main result to obstruct Dehn surgeries on knots from being rationally cobordant to lens spaces.

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 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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