Khovanov-Rozansky homology for infinite multi-colored braids

Abstract

We define a limiting ${\mathfrak{sl}}_N$ Khovanov-Rozansky homology for semi-infinite positive multi-colored braids, and we show that this limiting homology categorifies a highest-weight projector for a large class of such braids. This effectively completes the extension of Cautis' similar result for infinite twist braids, begun in our earlier papers with Islambouli and Abel. We also present several similar results for other families of semi-infinite and bi-infinite multi-colored braids.

arXiv comment37 pages, 13 figures

References in corpus (10)

• Khovanov's homology for tangles and cobordisms
• Webs and quantum skew Howe duality
• A colored sl(N)-homology for links in S^3
• Quantum (sl_n, \land V_n) link invariant and matrix factorizations
• Categorified Young symmetrizers and stable homology of torus links
• A categorification of the stable SU(2) Witten-Reshetikhin-Turaev invariant of links in S2 x S1
• A Categorification of Quantum sl_3 Projectors and the sl_3 Reshetikhin-Turaev Invariant of Tangles
• Skein Modules from Skew Howe Duality and Affine Extensions
• Colored Khovanov-Rozansky homology for infinite braids
• Khovanov homology for links in ${\#}^r(S^2\times S^1)$

Cited by in corpus (4)

• Khovanov polynomials for satellites and asymptotic adjoint polynomials
• Towards tangle calculus for Khovanov polynomials
• Planar decomposition of bipartite HOMFLY polynomials in symmetric representations
• Khovanov-Rozansky cycle calculus for bipartite links