scholarly journals Arbitrarily large torsion in Khovanov cohomology

2021 ◽  
Author(s):  
Sujoy Mukherjee ◽  
Dirk Schütz
Keyword(s):  
Khovanov Cohomology

scholarly journals Torsion calculations in Khovanov cohomology

2020 ◽  
Vol 29 (08) ◽  
pp. 2071001
Author(s):  
Dirk Schütz
Keyword(s):  
Torus Knots ◽  
Khovanov Cohomology

We obtain information on torsion in Khovanov cohomology by performing calculations directly over [Formula: see text] for [Formula: see text] prime and [Formula: see text]. In particular, we get that the torus knots [Formula: see text] and [Formula: see text] contain torsion of order [Formula: see text] and [Formula: see text] in their Khovanov cohomology.

scholarly journals A geometric description of the extreme Khovanov cohomology

2017 ◽  
Vol 148 (3) ◽  
pp. 541-557 ◽  
Author(s):  
J. González-Meneses ◽  
P. M. G. Manchón ◽  
M. Silvero
Keyword(s):  
Simplicial Complex ◽  
Geometric Description ◽  
Khovanov Cohomology ◽  
Cohomology Modules

We prove that the potential extreme Khovanov cohomology of a link is the cohomology of the independence simplicial complex of its Lando graph. We also provide a family of knots having as many non-trivial extreme Khovanov cohomology modules as desired, that is, examples of H-thick knots that are as far from being H-thin as desired.

scholarly journals The Fukaya category of the pillowcase, traceless character varieties, and Khovanov cohomology

2020 ◽  
Vol 373 (12) ◽  
pp. 8391-8437
Author(s):  
Matthew Hedden ◽  
Christopher M. Herald ◽  
Matthew Hogancamp ◽  
Paul Kirk
Keyword(s):  
Fukaya Category ◽  
Character Varieties ◽  
Khovanov Cohomology

scholarly journals A FAST ALGORITHM FOR CALCULATING S-INVARIANTS

2020 ◽  
pp. 1-22
Author(s):  
DIRK SCHÜTZ
Keyword(s):  
Fast Algorithm ◽  
Slight Modification ◽  
Divide And Conquer ◽  
Khovanov Cohomology

Abstract We use the divide-and-conquer and scanning algorithms for calculating Khovanov cohomology directly on the Lee- or Bar-Natan deformations of the Khovanov complex to give an alternative way to compute Rasmussen s-invariants of knots. By disregarding generators away from homological degree 0, we can considerably improve the efficiency of the algorithm. With a slight modification, we can also apply it to a refinement of Lipshitz–Sarkar.

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