无限辫的Khovanov同调

IF 1 2区数学 Q1 MATHEMATICS Quantum Topology Pub Date : 2016-10-14 DOI:10.4171/QT/114

Gabriel Islambouli, Michael Willis

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引用次数: 7

摘要

证明了任意无限正辫的极限Khovanov链复合体是Jones-Wenzl投影器的一类。利用无限环面编织的极限复合体，推广了Lev Rozansky关于Jones-Wenzl投影仪的分类。对于此类辫状体闭包的极限Lipshitz-Sarkar-Khovanov同伦类型，我们也给出了类似的结果。扩展到更一般的无限辫子也被考虑。

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The Khovanov homology of infinite braids

We show that the limiting Khovanov chain complex of any infinite positive braid categorifies the Jones-Wenzl projector. This result extends Lev Rozansky's categorification of the Jones-Wenzl projectors using the limiting complex of infinite torus braids. We also show a similar result for the limiting Lipshitz-Sarkar-Khovanov homotopy types of the closures of such braids. Extensions to more general infinite braids are also considered.

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来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.