Khovanov–Rozansky homology for infinite multicolored braids. (8th October 2021)

• Record Type: Journal Article
• Authors: Willis, Michael
• Is Part Of: Canadian journal of mathematics. Volume 73:Number 5(2021)
• Page Start: 1239
• Page End: 1277
• Publication Date: 2021-10-08
• Subjects: 57M25 -- 57M27; Khovanov homology -- colored Khovanov homology -- Khovanov–Rozansky homology -- colored Khovanov–Rozansky homology -- colored link homology -- categorified projector -- infinite twist -- infinite braids; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/S0008414X20000437
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: We define a limiting ${\mathfrak {sl}_N}$ Khovanov–Rozansky homology for semi-infinite positive multicolored braids. For a large class of such braids, we show that this limiting homology categorifies a highest-weight projector in the tensor product of fundamental representations determined by the coloring of the braid. 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 multicolored braids.