|
|||||
|
|
|
|
|
|
|
|
|
Khovanov homology is a
skew Howe $2$–representation of categorified quantum
$\mathfrak{sl}_m$
Aaron D Lauda, Hoel Queffelec and David E V Rose |
|
Algebraic & Geometric Topology 15 (2015) 2517–2608
|
Abstract |
|
We show that Khovanov homology (and its variant) can be understood in the context of higher representation theory. Specifically, we show that the combinatorially defined foam constructions of these theories arise as a family of –representations of categorified quantum via categorical skew Howe duality. Utilizing Cautis–Rozansky categorified clasps we also obtain a unified construction of foam-based categorifications of Jones–Wenzl projectors and their analogs purely from the higher representation theory of categorified quantum groups. In the case, this work reveals the importance of a modified class of foams introduced by Christian Blanchet which in turn suggest a similar modified version of the foam category introduced here. |
Keywords
Khovanov homology, categorified quantum groups, cobordism
categories, foam categories, skew Howe duality, link
homology
|
Mathematical Subject Classification 2010
Primary: 81R50
Secondary: 17B37, 57M25, 18G60
|
References |
Publication
Received: 31 July 2013
Revised: 1 December 2014
Accepted: 14 December 2014
Published: 10 December 2015
|
Authors |
| Aaron D Lauda | |
| Department of Mathematics University of Southern California Los Angeles, CA 90089 USA |
|
| Hoel Queffelec | |
| CNRS Institut Montpelliérain Alexander Grothendieck Université de Montpellier 34095 Montpellier Cedex 5 France |
|
| David E V Rose | |
| Department of Mathematics University of Southern California Los Angeles, CA 90089 USA |
|
|
