论文标题
soergel双模型和基质因化
Soergel bimodules and matrix factorizations
论文作者
论文摘要
我们建立了Khovanov-Rozansky Triply分级链接同源性与作者引起的几何分级同源性之间的同构。因此，我们提供了对Khovanov-Rozansky的同源性的解释，该同源物是将辫子$β$关闭为$ \ Mathbb {c}^*\ times \ times \ times \ mathbb {c}^*$ - equivariant sheaf $ tr（β）$ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert $ hilbert n（c） Gorsky-Nogut-Rasmussen猜想的一种版本\ cite {gorskynegutrasmussen16}。结果，我们证明了结的Khovanov-Rozansky同源性满足了Dunfield-Gukov-Rasmussen \ Cite \ cite {DunfieldGukovrasmussen06}猜想的$ q \ t/q $对称性。我们还采用了主要结果来计算圆环链接的Khovanov-Rozansky同源性。
We establish an isomorphism between the Khovanov-Rozansky triply graded link homology and the geometric triply graded homology due to the authors. Hence we provide an interpretation of the Khovanov-Rozansky homology of the closure of a braid $β$ as the space of derived sections of a $\mathbb{C}^*\times \mathbb{C}^*$- equivariant sheaf $Tr(β)$ on the Hilbert scheme $Hilb_n(\mathbb{C}^2)$, thus proving a version of Gorsky-Negut-Rasmussen conjecture \cite{GorskyNegutRasmussen16}. As a consequence we prove that Khovanov-Rozansky homology of knots satisfies the $q\to t/q$ symmetry conjectured by Dunfield-Gukov-Rasmussen \cite{DunfieldGukovRasmussen06}. We also apply our main result to compute the Khovanov-Rozansky homology of torus links.
