Surgery obstructions from Khovanov homology

Details Surgery obstructions from Khovanov homology Surgery obstructions from Khovanov homology

2008-07-09

arxiv.org/abs/0807.1341v4

Mathematics

Geometric Topology

53 pages, 19 figures. Version 2: Minor revisions. Updated references and added a new example. Version 3: Revised and expanded

Scientific paper

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.

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