Categorified sl(N) invariants of colored rational tangles

Abstract

We use categorical skew Howe duality to find recursion rules that compute categorified sl(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.

45 pages, many figures, uses dcpic.sty, v2: minor changes and new example 51

Cited by in corpus (4)

• Rational links and DT invariants of quivers
• Tangle addition and the knots-quivers correspondence
• ${\mathfrak{gl}}_n$-webs, categorification and Khovanov-Rozansky homologies
• q-holonomic formulas for colored HOMFLY polynomials of 2-bridge links