Torsion of Khovanov homology

By A. Shumakovitch. 2014

121 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7dc7891c2238fe04e5b1fca6136a4c9bafc626d0

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Man and machine thinking about the smooth 4-dimensional Poincaré conjecture (2009, result): “Extensive computations by Shumakovitch [40], [41], the authors and others support this conjecture, and it also holds for our examples (see below).”
Homological thickness and stability of torus knots (2005, methodology): “q) = Hi,j(Dp,p). Furthermore, by applying (11) (and then (9)) repeatedly we obtain Hi,j(Dp,p) = Hi,j+p−3(D 3,4) for i = 0,1,2,3,4. Finally, the homology of the last torus knot is well-known, see e.g. [27]-knot 8 19, and thus we obtain the required result. 5 Further thickness results Even though we h”
Spanning trees and Khovanov homology (2006, methodology): “shown with (u,v)-gradings, which determine the (p,q)-gradings for the spectral sequence. 7 Alternating and almost alternating links We give a simple new proof for theorems of Lee [6] and Shumakovitch [11] for the reduced Khovanov homology using the spanning tree complex. Theorem 12 The reduced Khova”
Khovanov's homology for tangles and cobordisms (2004, background): “Readers familiar with [Kh3, Sh , BN] will notice that every “knight move” in the array describing bQ rj gets replaced by a “tetris piece” in the array for bF2 rj and by a “shifted pawn move” in the array for b3rj, while the special pawn in column 0 of bQ rj stays put for b F2 rj and gets replaced b”
A remark on rasmussen's invariant of knots (2005, methodology): “[7] A. Shumakovitch, Torsion of the Khovanov homology, math.”
Knot polynomials and knot homologies (2005, background): “onent of ∂r is the one which takes q7t2 to q7t3. It is not diﬃcult to see that this component is multiplication by 2. Remark: In fact, it follows from work of Ozsv´ath and Szabo´ [25] or Shumakovitch [33] that the map ∂r is always congruent to 0 mod 2. 4.4 The δ grading and alternating links. Just a”