Year: 2025
Type: article
Abstract: A conjecture of Shumakovitch states that every nontrivial knot has 2-torsion in its Khovanov homology.We show that if a knot K has no 2-torsion in its Khovanov homology, then the rank of its reduced Khovanov homology is minimal among all knots obtainable from K by a proper rational tangle replacement.It follows, for example, that unknotting number 1 knots have 2-torsion in their Khovanov homology.57K18
Source: Algebraic & Geometric Topology
Authors: Onkar Singh Gujral, Joshua Wang
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: National Science Foundation
OpenAlex ID: W4415815744