论文标题
来自镜子对称性的同源结不变
Homological Knot Invariants from Mirror Symmetry
论文作者
论文摘要
1999年，科瓦诺夫（Khovanov）表明，一种称为琼斯多项式的链接不变是同源理论的欧拉（Euler）特征。结的分类问题是找到一个结同源组的一般结构，并解释其含义 - 它们的同源性是什么？ 由Kontsevich于1994年制定的同源镜子对称性自然会产生许多同源不变的宿主。但是，通常，它会导致不变的问题，而这些问题对当前的问题没有特别的兴趣。 我最近表明，有一个新的镜子对歧管的家族，同源镜子对称性确实导致了有趣的不变性并解决了结的分类问题。对于任何简单的谎言代数，以及某些lie superalgebras，可显式的不变性可显式计算。
In 1999, Khovanov showed that a link invariant known as the Jones polynomial is the Euler characteristic of a homology theory. The knot categorification problem is to find a general construction of knot homology groups, and to explain their meaning -- what are they homologies of? Homological mirror symmetry, formulated by Kontsevich in 1994, naturally produces hosts of homological invariants. Typically though, it leads to invariants which have no particular interest outside of the problem at hand. I showed recently that there is a new family of mirror pairs of manifolds, for which homological mirror symmetry does lead to interesting invariants and solves the knot categorification problem. The resulting invariants are computable explicitly for any simple Lie algebra, and certain Lie superalgebras.
