Topology Atlas | Conferences

Knots in Washington XLV
December 8-10, 2017
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

Conference Homepage


A rank inequality for the annular Khovanov homology of 2-periodic links
by
Melissa Zhang
Boston College

Abstract

A link in the 3-sphere exhibiting 2-fold symmetry can be viewed naturally as embedded in a thickened annulus. We show that there is a rank inequality between the annular Khovanov homology of the periodic (or symmetric) link and that of its quotient link, without using any heavy algebraic machinery. The rank inequality splits along the quantum and sl2 weight space gradings, and decategorifies to Murasugi-like congruences for annular links. Curiously, our method may also lead to a rank inequality between the Khovanov homologies of these links; we discuss partial results on this front.

Date received: November 29, 2017

Copyright © 2017 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cboj-18.