scholarly journals Torus link homology and the nabla operator

2018 ◽  
Vol 154 ◽  
pp. 129-144 ◽  
Author(s):  
A.T. Wilson
Keyword(s):  
Nabla Operator ◽  
Link Homology

scholarly journals Matrix factorizations and link homology II

2008 ◽  
Vol 12 (3) ◽  
pp. 1387-1425 ◽  
Author(s):  
Mikhail Khovanov ◽  
Lev Rozansky
Keyword(s):  
Matrix Factorizations ◽  
Link Homology

scholarly journals Matrix factorizations and link homology

2008 ◽  
Vol 199 (1) ◽  
pp. 1-91 ◽  
Author(s):  
Mikhail Khovanov ◽  
Lev Rozansky
Keyword(s):  
Matrix Factorizations ◽  
Link Homology

scholarly journals TRIPLY-GRADED LINK HOMOLOGY AND HOCHSCHILD HOMOLOGY OF SOERGEL BIMODULES

2007 ◽  
Vol 18 (08) ◽  
pp. 869-885 ◽  
Author(s):  
MIKHAIL KHOVANOV
Keyword(s):  
Group Action ◽  
Braid Group ◽  
Polynomial Algebra ◽  
Homology Theory ◽  
Hochschild Homology ◽  
Polynomial Algebras ◽  
Homology Groups ◽  
Link Homology ◽  
Soergel Bimodules ◽  
Braid Group Action

We consider a class of bimodules over polynomial algebras which were originally introduced by Soergel in relation to the Kazhdan–Lusztig theory, and which describe a direct summand of the category of Harish–Chandra modules for sl(n). Rouquier used Soergel bimodules to construct a braid group action on the homotopy category of complexes of modules over a polynomial algebra. We apply Hochschild homology to Rouquier's complexes and produce triply-graded homology groups associated to a braid. These groups turn out to be isomorphic to the groups previously defined by Lev Rozansky and the author, which depend, up to isomorphism and overall shift, only on the closure of the braid. Consequently, our construction produces a homology theory for links.

scholarly journals The 1,2-coloured HOMFLY-PT link homology

2011 ◽  
Vol 363 (04) ◽  
pp. 2091-2091 ◽  
Author(s):  
Marco Mackaay ◽  
Marko Stošić ◽  
Pedro Vaz
Keyword(s):  
Link Homology

Link Homology in 4-Manifolds

1996 ◽  
Vol 28 (4) ◽  
pp. 409-412 ◽  
Author(s):  
Akira Yasuhara
Keyword(s):  
Link Homology

scholarly journals A KHOVANOV TYPE INVARIANT DERIVED FROM AN UNORIENTED HQFT FOR LINKS IN THICKENED SURFACES

2013 ◽  
Vol 24 (10) ◽  
pp. 1350078 ◽  
Author(s):  
KEIJI TAGAMI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Equivalence Class ◽  
Chain Complex ◽  
Quantum Field ◽  
Link Homology ◽  
Stable Equivalence ◽  
Reidemeister Moves ◽  
Link Diagrams ◽  
Topological Quantum

Two link diagrams on compact surfaces are strongly equivalent if they are related by Reidemeister moves and orientation preserving homeomorphisms of the surfaces. They are stably equivalent if they are related by the two previous operations and adding or removing handles. Turaev and Turner constructed a link homology for each stable equivalence class by applying an unoriented topological quantum field theory (TQFT) to a geometric chain complex similar to Bar-Natan's one. In this paper, by using an unoriented homotopy quantum field theory (HQFT), we construct a link homology for each strong equivalence class. Moreover, our homology yields an invariant of links in the oriented I-bundle of a compact surface.

scholarly journals Link homology and Frobenius extensions

2006 ◽  
Vol 190 ◽  
pp. 179-190 ◽  
Author(s):  
Mikhail Khovanov
Keyword(s):  
Link Homology

scholarly journals Simplicial homotopy theory, link homology and Khovanov homology

2018 ◽  
Vol 27 (07) ◽  
pp. 1841002
Author(s):  
Louis H. Kauffman
Keyword(s):  
Homotopy Theory ◽  
Khovanov Homology ◽  
Frobenius Algebra ◽  
Link Diagram ◽  
Link Homology ◽  
Simplicial Homotopy ◽  
Simplicial Methods

This paper shows how, in principle, simplicial methods, including the well-known Dold–Kan construction can be applied to convert link homology theories into homotopy theories. The paper studies particularly the case of Khovanov homology and shows how simplicial structures are implicit in the construction of the Khovanov complex from a link diagram and how the homology of the Khovanov category, with coefficients in an appropriate Frobenius algebra, is related to Khovanov homology. This Khovanov category leads to simplicial groups satisfying the Kan condition that are relevant to a homotopy theory for Khovanov homology.

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