A rank inequality for the annular Khovanov homology of 2-periodic links

作者：Zhang Melissa^*

来源：Algebraic and Geometric Topology, 2018, 18(2): 1147-1194.

DOI：10.2140/agt.2018.18.1147

For a 2-periodic link (L) over tilde in the thickened annulus and its quotient link L, we exhibit a spectral sequence with
E-1 congruent to AKh((L) over tilde) circle times(F) F[theta, theta(-1)] paired right arrows E-infinity congruent to AKh(L) circle times(F) F[theta, theta(-1)].
This spectral sequence splits along quantum and sl(2) weight-space gradings, proving a rank inequality rkAKh(j ,k) (L) <= rkAKh(2)(j-k, k) ((L) over tilde) for every pair of quantum and sl(2) weight-space gradings (j, k). We also present a few decategorified consequences and discuss partial results toward a similar statement for the Khovanov homology of 2-periodic links, as well as some frameworks for obstructing 2-periodicity in links.

• 出版日期2018