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Remarks on coloured triply graded link invariants

Sabin Cautis

Algebraic & Geometric Topology 17 (2017) 3811–3836

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.

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