scholarly journals A link-splitting spectral sequence in Khovanov homology

2015 ◽  
Vol 164 (5) ◽  
pp. 801-841 ◽  
Author(s):  
Joshua Batson ◽  
Cotton Seed
Keyword(s):  
Spectral Sequence ◽  
Khovanov Homology

scholarly journals Curved Rickard complexes and link homologies

2020 ◽  
Vol 2020 (769) ◽  
pp. 87-119
Author(s):  
Sabin Cautis ◽  
Aaron D. Lauda ◽  
Joshua Sussan
Keyword(s):  
Spectral Sequence ◽  
Quantum Groups ◽  
Braid Group ◽  
Derived Categories ◽  
Duke Math ◽  
Khovanov Homology ◽  
Hilbert Schemes ◽  
Coherent Sheaves ◽  
Knot Homology ◽  
Original Motivation

AbstractRickard complexes in the context of categorified quantum groups can be used to construct braid group actions. We define and study certain natural deformations of these complexes which we call curved Rickard complexes. One application is to obtain deformations of link homologies which generalize those of Batson–Seed [3] [J. Batson and C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J. 164 2015, 5, 801–841] and Gorsky–Hogancamp [E. Gorsky and M. Hogancamp, Hilbert schemes and y-ification of Khovanov–Rozansky homology, preprint 2017] to arbitrary representations/partitions. Another is to relate the deformed homology defined algebro-geometrically in [S. Cautis and J. Kamnitzer, Knot homology via derived categories of coherent sheaves IV, colored links, Quantum Topol. 8 2017, 2, 381–411] to categorified quantum groups (this was the original motivation for this paper).

scholarly journals ON THE QUANTUM FILTRATION OF THE UNIVERSAL sl(2) FOAM COHOMOLOGY

2012 ◽  
Vol 21 (03) ◽  
pp. 1250023 ◽  
Author(s):  
CARMEN CAPRAU
Keyword(s):  
Lower Bound ◽  
Spectral Sequence ◽  
Khovanov Homology ◽  
Reidemeister Moves

We investigate the filtered theory corresponding to the universal sl(2) foam cohomology [Formula: see text] for links, where a, h ∈ ℂ. We show that there is a spectral sequence converging to [Formula: see text] which is invariant under the Reidemeister moves, and whose E1 term is isomorphic to Khovanov homology. This spectral sequence can be used to obtain from the foam perspective an analogue of the Rasmussen invariant and a lower bound for the slice genus of a knot.

scholarly journals Khovanov homology and knot Floer homology for pointed links

2017 ◽  
Vol 26 (02) ◽  
pp. 1740004 ◽  
Author(s):  
John A. Baldwin ◽  
Adam Simon Levine ◽  
Sucharit Sarkar
Keyword(s):  
Spectral Sequence ◽  
Floer Homology ◽  
Khovanov Homology ◽  
Knot Floer Homology ◽  
Text Page ◽  
Text Component

A well-known conjecture states that for any [Formula: see text]-component link [Formula: see text] in [Formula: see text], the rank of the knot Floer homology of [Formula: see text] (over any field) is less than or equal to [Formula: see text] times the rank of the reduced Khovanov homology of [Formula: see text]. In this paper, we describe a framework that might be used to prove this conjecture. We construct a modified version of Khovanov homology for links with multiple basepoints and show that it mimics the behavior of knot Floer homology. We also introduce a new spectral sequence converging to knot Floer homology whose [Formula: see text] page is conjecturally isomorphic to our new version of Khovanov homology; this would prove that the conjecture stated above holds over the field [Formula: see text].

scholarly journals KHOVANOV HOMOLOGY AND RASMUSSEN'S s-INVARIANTS FOR PRETZEL KNOTS

2010 ◽  
Vol 19 (09) ◽  
pp. 1183-1204 ◽  
Author(s):  
RYOHEI SUZUKI
Keyword(s):  
Spectral Sequence ◽  
Khovanov Homology ◽  
Pretzel Knots ◽  
Almost All

We calculate the rational Khovanov homology of a class of pretzel knots by using the spectral sequence constructed by Turner. Moreover, we determine Rasmussen's s-invariant of almost all pretzel knots P(p, q, r) by using Turner's spectral sequence, a sharper slice-Bennequin inequality, and a skein inequality.

scholarly journals A geometric spectral sequence in Khovanov homology

2015 ◽  
Vol 8 (4) ◽  
pp. 1017-1044 ◽  
Author(s):  
Zoltán Szabó
Keyword(s):  
Spectral Sequence ◽  
Khovanov Homology

scholarly journals A perturbation of the geometric spectral sequence in Khovanov homology

10.4171/qt/97 ◽  
2017 ◽  
Vol 8 (3) ◽  
pp. 571-628 ◽  
Author(s):  
Sucharit Sarkar ◽  
Cotton Seed ◽  
Zoltán Szabó
Keyword(s):  
Spectral Sequence ◽  
Khovanov Homology
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