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Abstract
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We explain how existing results (such as categorical
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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Keywords
knot homology, triply graded, categorical actions, Soergel
bimodules
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 16T99
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Publication
Received: 8 February 2017
Revised: 16 May 2017
Accepted: 12 June 2017
Published: 4 October 2017
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