Remarks on coloured triply graded link invariants
Sabin Cautis
TL;DR
This paper presents a new triply graded link invariant that categorifies the HOMFLY polynomial for links with arbitrary colorings, utilizing categorical actions, braid group actions, and infinite twists.
Contribution
It introduces a novel categorification approach for the HOMFLY polynomial using a triply graded invariant based on categorified clasps and infinite twists.
Findings
Defines a triply graded link invariant for colored links
Uses categorified HOMFLY clasp via cabling and infinite twists
Discusses differentials and related structures
Abstract
We explain how existing results (such as categorical sl(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.
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