An endomorphism of the Khovanov invariant

By Eun Soo Lee. 2002

127 citations recorded by the source corpus.

Abstract We construct an endomorphism of the Khovanov invariant to prove H-thinness and pairing phenomena of the invariants for alternating links. As a consequence, it follows that the Khovanov invariant of an oriented nonsplit alternating link is determined by its Jones polynomial, signature, and the linking numbers of its components.

View Paper: https://www.semanticscholar.org/paper/429a9b5387e25137341bda65e6b140d17e7c0762

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Citations in the corpus

• Functoriality of colored link homologies (2017, methodology): “They give rise to a deformed link homology theory that is analogous to Lee’s deformation [32] of Khovanov homology.”
• Some differentials on Khovanov–Rozansky homology (2006, background): “In some sense, these sequences are all generalizations of Lee’s original spectral sequence [16] for the Khovanov homology.”
• Deformations of colored sl(N) link homologies via foams (2015, background): “ a powerful topological invariant, leading e.g. to Rasmussen’s combinatorial proof of the Milnor conjecture on the slice genus of torus knots [Ras2]. Rasmussen’s work built on earlier results of Lee, [Lee], who studied a deformed version of Khovanov’s link invariant. Khovanov’s theory is controlled ”
• The Karoubi envelope and Lee’s degeneration of Khovanov homology (2006, methodology): “s, pagination and layout may vary from AGT published version The Karoubi envelope and Lee’s degeneration of Khovanov homology DROR BAR-NATAN SCOTT MORRISON We give a simple proof of Lee’s result from [5], that the dimension of the Lee variant of the Khovanov homology of a c–component link is 2c, reg”
• Clasp technology to knot homology via the affine Grassmannian (2012, background): “ matrix factorizations [Wu, Y] and foams [MSV, LQR, QR] are known (or at least expected to) fit in this picture. The argument above shows they are isomorphic. 1.5. Lee-like deformations. Lee defined in [Lee] a modification of Khovanov homology (now called Lee homology) and showed that there exists a sp”
• The chromatic polynomial of fatgraphs and its categorification (2005, background): “re additive under the connect 22 sum, we see that these two invariants are equal for both our associated links. However, the linking numbers do change under the operations. By Theorems 1.2 and 4.5 of [26] and Corollary A.2 of [16], we see that it is enough to show that if the components of each of t”
• A spectral sequence for Khovanov homology with an application to (3,q)–torus links (2006, background): “Since Lee’s homology is easy to compute [5] (depending only on the linking matrix of the link) one can, by reverse engineering, obtain some information about Khovanov homology itself.”