Instantons and Bar-Natan homology
نویسندگان
چکیده
A spectral sequence is established whose $E_{2}$ page Bar-Natan's variant of Khovanov homology and which abuts to a deformation instanton for knots links. This arises as specialization characteristic-2 version $F_{5}$ in Khovanov's classification.
منابع مشابه
Coloured Stable Bar-natan Link Homology
We compute the stable Bar-Natan link homology of oriented framed links coloured by irreducible representations of Uq(sl2).
متن کاملDror Bar - Natan : Mathematical
(150107) l : ApGq Ñ ApGq bApGq wrong sketch: If V is doubly filtered, the associated graded of the diagonally-associated single filtration of V is isomorphic to the diagonal single-gradation of the associated doubly-graded of V . False. Take V Qxx, yy, F0,0 F1,0 F0,1 V , F2,0 xxy, F1,1 F0,2 xyy. Then 0 xrxsy V1,0 ` V0,1 V1 0. ApG Hq ApGqbApHq as the associated single filtration of the double fi...
متن کاملThe Bar-Natan Skein Module of the Solid Torus and the Homology of (n,n) Springer Varieties
This paper establishes an isomorphism between the Bar-Natan skein module of the solid torus with a particular boundary curve system and the homology of the (n, n) Springer variety. The results build on Khovanov’s work with crossingless matchings and the cohomology of the (n, n) Springer variety. We also give a formula for comultiplication in the Bar-Natan skein module for this specific three-ma...
متن کاملCalculating Bar-natan’s Characteristic Two Khovanov Homology
We investigate Bar-Natan’s characteristic two Khovanov link homology theory studying both the filtered and bi-graded theories. The filtered theory is computed explicitly and the bi-graded theory analysed by setting up a family of spectral sequences. The E2-pages can be described in terms of groups arising from the action of a certain endomorphism on F2-Khovanov homology. Some simple consequence...
متن کاملBar-natan’s Khovanov Homology for Coloured Links
Using Bar-Natan’s Khovanov homology we define a homology theory for links whose components are labelled by irreducible representations of Uq(sl2). We then compute this explicitly.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2021
ISSN: ['0010-437X', '1570-5846']
DOI: https://doi.org/10.1112/s0010437x2000768x