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.

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

References in corpus (5)

• On the Khovanov and knot Floer homologies of quasi-alternating links
• Lens space surgeries and L-space homology spheres
• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• Finite surgeries on three-tangle pretzel knots
• Cyclic and finite surgeries on Montesinos knots

Cited by in corpus (12)

• Khovanov homology, sutured Floer homology, and annular links
• On L-spaces and left-orderable fundamental groups
• Finite surgeries on three-tangle pretzel knots
• Cyclic and finite surgeries on Montesinos knots
• Tables of quasi-alternating knots with at most 12 crossings
• A remark on Khovanov homology and two-fold branched covers
• Immersed surfaces and Seifert fibered surgery on Montesinos knots
• Quasi-alternating links and odd homology: computations and conjectures
• On Khovanov-Seidel quiver algebras and bordered Floer homology
• Graphical methods establishing nontriviality of state cycle Khovanov homology classes
• The Khovanov width of twisted links and closed 3-braids
• Cosmetic operations and Khovanov multicurves