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Abstract
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We use categorical skew Howe duality to find recursion rules that compute categorified
invariants of rational tangles colored by exterior powers of the standard
representation. Further, we offer a geometric interpretation of these rules which
suggests a connection to Floer theory. Along the way we make progress towards two
conjectures about the colored HOMFLY homology of rational links and discuss
consequences for the corresponding decategorified invariants.
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Keywords
categorification, rational tangles, link homology, HOMFLY
homology
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Mathematical Subject Classification 2010
Primary: 57M25, 81R50
Secondary: 57R58
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Publication
Received: 16 October 2014
Revised: 18 April 2015
Accepted: 26 May 2015
Published: 23 February 2016
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