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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Remarks on coloured triply graded link invariants

Sabin Cautis

Algebraic & Geometric Topology 17 (2017) 3811–3836
Abstract

We explain how existing results (such as categorical sln actions, associated braid group actions and infinite twists) can be used to define a triply graded link invariant which categorifies the homfly polynomial of links coloured by arbitrary partitions. The construction uses a categorified homfly clasp defined via cabling and infinite twists. We briefly discuss differentials and speculate on related structures.

Keywords
knot homology, triply graded, categorical actions, Soergel bimodules
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 16T99
References
Publication
Received: 8 February 2017
Revised: 16 May 2017
Accepted: 12 June 2017
Published: 4 October 2017
Authors
Sabin Cautis
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada