Surgery obstructions from Khovanov homology
Abstract
For a 3-manifold with torus boundary admitting an appropriate involution, we show that Khovanov homology provides obstructions to certain exceptional Dehn fillings. For example, given a strongly invertible knot in S^3, we give obstructions to lens space surgeries, as well as obstructions to surgeries with finite fundamental group. These obstructions are based on homological width in Khovanov homology, and in the case of finite fundamental group depend on a calculation of the homological width for a family of Montesinos links.
Cite
@article{arxiv.0807.1341,
title = {Surgery obstructions from Khovanov homology},
author = {Liam Watson},
journal= {arXiv preprint arXiv:0807.1341},
year = {2011}
}
Comments
53 pages, 19 figures. Version 2: Minor revisions. Updated references and added a new example. Version 3: Revised and expanded version. Includes new results and examples. Version 4: Revised per referee's comments, including a new section treating lower bounds for homological width. This version to appear in Selecta Mathematica