论文标题
关于Khovanov同源性和相关不变的
On Khovanov Homology and Related Invariants
论文作者
论文摘要
本文首先对Khovanov同源性与低维拓扑的某些应用进行了调查，并着眼于将这些结果扩展到$ \ Mathfrak {SL}（n）$同源性。我们将Levine和Zemke的功能界一致性从Khovanov同源性扩展到$ \ Mathfrak {sl}（n）$同源性，包括$ n \ geq 2 $，包括Universal $ \ Mathfrak {sl}（2）$和$ \ Mathfrak {2）$和Mathfrak {Slfrak {Sl}（3）$ homology prology tealorie。受Alishahi和Dowlin的范围的启发，我们对来自Khovanov同源性的无结数字并依赖于频谱序列参数的启发，我们对结的交替数量产生了界限。 Lee和Bar-Natan光谱序列还提供了Turaev属的下限。
This paper begins with a survey of some applications of Khovanov homology to low-dimensional topology, with an eye toward extending these results to $\mathfrak{sl}(n)$ homologies. We extend Levine and Zemke's ribbon concordance obstruction from Khovanov homology to $\mathfrak{sl}(n)$ homology for $n \geq 2$, including the universal $\mathfrak{sl}(2)$ and $\mathfrak{sl}(3)$ homology theories. Inspired by Alishahi and Dowlin's bounds for the unknotting number coming from Khovanov homology and relying on spectral sequence arguments, we produce bounds on the alternation number of a knot. Lee and Bar-Natan spectral sequences also provide lower bounds on Turaev genus.
