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arXiv · 2409.02940

Khovanov-Rozansky homologies, Bott-Samelson spaces and twisted cohomology

Tomas Mejia-Gomez
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Abstract

By means of Rasmussen's formulation of Khovanov-Rozansky homology originally given over $\mathbb{Q}$ in arXiv:math/0607544, we compare different flavors of $\mathfrak{sl}(n)$ link homology with the link invariants obtained by Kitchloo in arXiv:1910.07444 via twistings of Borel equivariant cohomology applied to the symmetry breaking spectra. In particular, we see how these geometric constructions based on Bott-Samelson varieties produce equivariant integral $\mathfrak{sl}(n)$ link homology with either specialized or universal potential.

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Tomas Mejia-Gomez. 2024-08-24. Khovanov-Rozansky homologies, Bott-Samelson spaces and twisted cohomology. https://arxiv.org/abs/2409.02940

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