Annular Khovanov homology and 2-periodic links

Geometry/topology Seminar

Melissa Zhang (Boston College)

Monday, April 2, 2018 -
3:15pm to 4:15pm
119 Physics

I will exhibit a spectral sequence from the annular Khovanov homology of a 2-periodic link to that of its quotient, which in turn proves rank inequalities and decategorifies to polynomial congruences. While previous work used heavier algebraic machinery to prove this rank inequality in a particular sl_2 weight space grading, we instead mimic Borel's construction of equivariant cohomology and employ grading considerations to give a combinatorial proof of the rank inequality for all quantum and sl_2 weight space gradings. Curiously, the same methods suggest a similar spectral sequence relating the Khovanov homology of a 2-periodic link and the annular Khovanov homology of its quotient link. We'll discuss partial results on this front.

Last updated: 2018/05/21 - 12:02am