Khovanov homology and the search for exotic 4-spheres
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| Title | Khovanov homology and the search for exotic 4-spheres |
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| Number of Parts | 10 |
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| License | You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor. |
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| Abstract | A well-known strategy to disprove the smooth 4D Poincare conjecture is to find a knot that bounds a disk in a homotopy 4-ball but not in the standard 4-ball. Freedman, Gompf, Morrison and Walker suggested that Rasmussenâ s invariant from Khovanov homology could be useful for this purpose. I will describe three recent results about this strategy: that it fails for Gluck twists (joint work with Marengon, Sarkar and Willis); that an analogue works for other 4-manifolds (joint work with Marengon and Piccirillo); and that 0-surgery homeomorphisms provide a large class of potential examples (joint work with Piccirillo). |
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