Remarks on coloured triply graded link invariants

Cautis, Sabin

doi:10.2140/agt.2017.17.3811

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Remarks on coloured triply graded link invariants

Sabin Cautis

Algebraic & Geometric Topology 17 (2017) 3811–3836

DOI: 10.2140/agt.2017.17.3811

Abstract

We explain how existing results (such as categorical ${s l}_{n}$ 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

Volume 17, issue 6 (2017)