#### 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
##### Abstract

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