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A generalized skein relation for Khovanov homology and a categorification of the θ-invariant
Proceedings of the Royal Society of Edinburgh Section A: Mathematics ( IF 1.3 ) Pub Date : 2020-11-05 , DOI: 10.1017/prm.2020.78
M. Chlouveraki , D. Goundaroulis , A. Kontogeorgis , S. Lambropoulou

The Jones polynomial is a famous link invariant that can be defined diagrammatically via a skein relation. Khovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation satisfied by the Khovanov homology. Thanks to this relation, we are able to generalize the Khovanov homology in order to obtain a categorification of the θ-invariant, which is itself a generalization of the Jones polynomial.

中文翻译:

Khovanov 同调的广义绞合关系和 θ 不变量的分类

琼斯多项式是一个著名的链接不变量,可以通过绞合关系以图表方式定义。Khovanov 同调是对琼斯多项式进行分类的更丰富的链接不变量。使用光谱序列,我们获得了由 Khovanov 同源性满足的绞合型关系。由于这种关系,我们能够推广 Khovanov 同调,以获得对θ-不变量,它本身就是琼斯多项式的推广。
更新日期:2020-11-05
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