Fast Khovanov homology computations

被引：92

作者：

Bar-Natan, Dror ^{[1
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2007年 / 16卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

categorification cobordism; divide and conquer; Jones polynomial; Kauffman bracket; Khovanov knot invariants; tangles;

D O I：

10.1142/S0218216507005294

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a local algorithm for Khovanov homology computations - that is, we explain how it is possible to "cancel" terms in the Khovanov complex associated with a (" local") tangle, hence canceling the many associated " global" terms in one swoosh early on. This leads to a dramatic improvement in computational efficiency. Thus our program can rapidly compute certain Khovanov homology groups that otherwise would have taken centuries to evaluate.

引用

页码：243 / 255

页数：13

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