Volume 16, issue 1 (2016)

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Categorified $\mathfrak{sl}_N$ invariants of colored rational tangles

Paul Wedrich

Algebraic & Geometric Topology 16 (2016) 427–482

We use categorical skew Howe duality to find recursion rules that compute categorified slN 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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categorification, rational tangles, link homology, HOMFLY homology
Mathematical Subject Classification 2010
Primary: 57M25, 81R50
Secondary: 57R58
Received: 16 October 2014
Revised: 18 April 2015
Accepted: 26 May 2015
Published: 23 February 2016
Paul Wedrich
Centre for Mathematical Sciences
University of Cambridge
Cambridge CB3 0WB