Categorified 𝔰𝔩N invariants of colored rational tangles

Wedrich, Paul

doi:10.2140/agt.2016.16.427

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

Paul Wedrich

Algebraic & Geometric Topology 16 (2016) 427–482

DOI: 10.2140/agt.2016.16.427

Abstract

We use categorical skew Howe duality to find recursion rules that compute categorified ${s l}_{N}$ 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.

Keywords

categorification, rational tangles, link homology, HOMFLY homology

Mathematical Subject Classification 2010

Primary: 57M25, 81R50

Secondary: 57R58

References

Publication

Received: 16 October 2014

Revised: 18 April 2015

Accepted: 26 May 2015

Published: 23 February 2016

Authors

Paul Wedrich
Centre for Mathematical Sciences University of Cambridge Cambridge CB3 0WB UK

Volume 16, issue 1 (2016)