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Joint Los Angeles Topology Seminar

Monday, November 7, 2022
5:30pm to 6:30pm
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Heegaard Floer homology, immersed curves, and chirally cosmetic surgeries
Konstantinos Varvarezos, Department of Mathematics, UCLA,

UCLA, Room 4645 in the Geology Building

Dehn surgery is a common method for obtaining 3-manifolds from knots. A pair of (Dehn) surgeries on a knot is called chirally cosmetic if the resulting manifolds are homeomorphic with opposite orientations. Making use of immersed curve formulations of Heegaard Floer invariants, we discuss new obstructions to the existence of such surgeries, which we apply to certain families of knots. In particular, it turns out that combined with previously known results, these obstructions are sufficient to completely classify chirally cosmetic surgeries on odd alternating pretzel knots. Furthermore, we are able to rule out cosmetic surgeries for L-space knots along slopes with opposite signs.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].