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Surgery obstructions from Khovanov homology

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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.

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Authors and Affiliations

  1. Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA, 90095, USA

    Liam Watson

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  1. Liam Watson
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Correspondence to Liam Watson.

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Supported by a Canada Graduate Scholarship (NSERC).

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Watson, L. Surgery obstructions from Khovanov homology. Sel. Math. New Ser. 18, 417–472 (2012). https://doi.org/10.1007/s00029-011-0070-2

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