Khovanov-Rozansky 同调、Bott-Samelson 空间和扭曲同调

arXiv - MATH - Quantum Algebra Pub Date : 2024-08-24 DOI:arxiv-2409.02940

Tomas Mejia-Gomez

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摘要

通过 Rasmussen 在 arXiv:math/0607544 中最初给出的关于 $\mathbb{Q}$ 的 Khovanov-Rozansky 同调的表述，我们比较了不同类型的 $\mathfrak{sl}(n)$ link homology 与 Kitchlooin 在 arXiv:1910.07444 中通过应用于对称破缺谱的 Borel 等变同调的扭转得到的 link invariants。特别是，我们将看到这些基于博特-萨缪尔森（Bott-Samelson）变体的几何构造如何产生具有专门或普遍势的等变积分$\mathfrak{sl}(n)$链接同调。

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

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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arXiv - MATH - Quantum Algebra

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