Categorified 𝔰𝔩N invariants of colored rational tangles

Wedrich, Paul¹

¹Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WB, UK

Algebraic and Geometric Topology, Tome 16 (2016) no. 1, pp. 427-482

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.427

Classification : 57M25, 81R50, 57R58
Keywords: categorification, rational tangles, link homology, HOMFLY homology

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