2 results
Khovanov–Rozansky homology for infinite multicolored braids
- Part of
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- Journal:
- Canadian Journal of Mathematics / Volume 73 / Issue 5 / October 2021
- Published online by Cambridge University Press:
- 08 June 2020, pp. 1239-1277
- Print publication:
- October 2021
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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.
On the computation of torus link homology
- Part of
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- Journal:
- Compositio Mathematica / Volume 155 / Issue 1 / January 2019
- Published online by Cambridge University Press:
- 23 November 2018, pp. 164-205
- Print publication:
- January 2019
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We introduce a new method for computing triply graded link homology, which is particularly well adapted to torus links. Our main application is to the
$(n,n)$-torus links, for which we give an exact answer for all 
$n$. In several cases, our computations verify conjectures of Gorsky et al. relating homology of torus links with Hilbert schemes.
