14 citations · 14 across the 3 of their papers we have counts for
6 papers · 1 filter
Torsion in Khovanov homology of homologically thin knots
Alexander N. Shumakovitch
We prove that every H-thin link has no -torsion for in its Khovanov homology. Together with previous results by Eun Soo Lee and the author, this implies th…
Khovanov homology theories and their applications
Alexander Shumakovitch
This is an expository paper discussing various versions of Khovanov homology theories, interrelations between them, their properties, and their applications to other areas of knot…
Patterns in odd Khovanov homology
Alexander N. Shumakovitch
We investigate properties of the odd Khovanov homology, compare and contrast them with those of the original (even) Khovanov homology, and discuss applications of the odd Khovanov…
Behavior of knot invariants under genus 2 mutation
Nathan M. Dunfield, Stavros Garoufalidis, Alexander Shumakovitch +1
Genus 2 mutation is the process of cutting a 3-manifold along an embedded closed genus 2 surface, twisting by the hyper-elliptic involution, and gluing back. This paper compares ge…
Rasmussen invariant, Slice-Bennequin inequality, and sliceness of knots
Alexander N. Shumakovitch
We use recently introduced Rasmussen invariant to find knots that are topologically locally-flatly slice but not smoothly slice. We note that this invariant can be used to give a c…
Casson invariant of knots associated with divides
Alexander Shumakovitch
I present a formula for the Casson invariant of knots associated with divides. The formula is written in terms of Arnold's invariants of pieces of the divide. Various corollaries a…