Khovanov Homology: Torsion and Thickness

By M. Asaeda, Józef H. Przytycki. 2004

68 citations recorded by the source corpus.

We partially solve the conjecture by A.Shumakovitch about torsion in the Khovanov homology of prime, non-split links in S^3. We give a size restriction on the Khovanov homology of almost alternating links. We relate the Khovanov homology of the connected sum of a link diagram and the Hopf link with the Khovanov homology of the diagram via a short exact sequence of homology which splits. Finally we show that our results can be adapted to reduced Khovanov homology and we show that there is a long exact sequence connecting reduced Khovanov homology with unreduced homology.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b6cdd0b5de306a054177e98b3cc396c0924c5372

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A Spanning Tree Model for Khovanov Homology (2004, background): “Przytycki [AP], who thus confirmed a conjecture of A.”
Spanning trees and Khovanov homology (2006, background): “hat the reduced Khovanov homology of an alternating knot is determined by its Jones polynomial and signature (Theorem 11). We also give simple new proofs for theorems by Lee [6] and Asaeda, Przytycki [2] on the support of Khovanov homology of alternating and k-almost alternating knots (Theorem 12). ”
On the spectral sequence from Khovanov homology to Heegaard Floer homology (2008, background): “Otherwise, K̃h(L) is supported in two consecutive δ-gradings, δ0 and δ1 = δ0 − 1, corresponding to the two groups K̃h(L0)[a, b] and K̃h(L1)[c, d], respectively [2, 6].”