5 citations · 18 across the 6 of their papers we have counts for
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On mutation and Khovanov homology
Abhijit Champanerkar, Ilya Kofman
It is conjectured that the Khovanov homology of a knot is invariant under mutation. In this paper, we review the spanning tree complex for Khovanov homology, and reformulate this c…
Twisting quasi-alternating links
Abhijit Champanerkar, Ilya Kofman
Quasi-alternating links are homologically thin for both Khovanov homology and knot Floer homology. We show that every quasi-alternating link gives rise to an infinite family of qua…
Spanning trees and Khovanov homology
Abhijit Champanerkar, Ilya Kofman
The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show there exists a complex generated by these sp…
On links with cyclotomic Jones polynomials
Abhijit Champanerkar, Ilya Kofman
We show that if {L_n} is any infinite sequence of links with twist number tau(L_n) and with cyclotomic Jones polynomials of increasing span, then lim sup tau(L_n)=infty. This impli…
Exceptional regions and associated exceptional hyperbolic 3-manifolds
Abhijit Champanerkar, Jacob Lewis, Max Lipyanskiy +2
A closed hyperbolic 3-manifold is exceptional if its shortest geodesic does not have an embedded tube of radius . D. Gabai, R. Meyerhoff and N. Thurston identified seven…
The next simplest hyperbolic knots
Abhijit Champanerkar, Ilya Kofman, Eric Patterson
We complete the project begun by Callahan, Dean and Weeks to identify all knots whose complements are in the SnapPea census of hyperbolic manifolds with seven or fewer tetrahedra.…