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
收藏
页码：243 / 255
页数：13
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