The Khovanov width of twisted links and closed 3-braids

Details The Khovanov width of twisted links and closed 3-braids The Khovanov width of twisted links and closed 3-braids

2009-01-15

arxiv.org/abs/0901.2196v2

Comment. Math. Helv. 86 (2011) no. 3, 675-706

Mathematics

Geometric Topology

24 pages, 14 figures

Scientific paper

Khovanov homology is a bigraded Z-module that categorifies the Jones polynomial. The support of Khovanov homology lies on a finite number of slope two lines with respect to the bigrading. The Khovanov width is essentially the largest horizontal distance between two such lines. We show that it is possible to generate infinite families of links with the same Khovanov width from link diagrams satisfying certain conditions. Consequently, we compute the Khovanov width for all closed 3-braids.

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