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Title: Cosmetic Surgeries on Knots and 3-Manifold Invariants
Authors: Varvarezos, Konstantinos
Advisors: Szabo, Zoltan
Contributors: Mathematics Department
Keywords: 3-manifolds
cosmetic surgery
Dehn surgery
Heegaard Floer homology
Subjects: Mathematics
Issue Date: 2022
Publisher: Princeton, NJ : Princeton University
Abstract: A common method of constructing 3-manifolds is via Dehn surgery on knots. A pair of surgeries on a knot is called purely cosmetic if the pair of resulting 3-manifolds are homeomorphic as oriented manifolds, whereas it is said to be chirally cosmetic if they result in homeomorphic manifolds with opposite orientations. An outstanding conjecture predicts that no nontrivial knots admit any purely cosmetic surgeries. We apply certain obstructions from Heegaard Floer homology to show that (nontrivial) knots which arise as the closure of a 3-stranded braid do not admit any purely cosmetic surgeries. Furthermore, we find new obstructions to the existence of chirally cosmetic surgeries coming from Heegaard Floer homology; in particular, we make use of immersed curve formulations of knot Floer homology and the corresponding surgery formula. Combining these with other obstructions involving finite type invariants, we completely classify chirally cosmetic surgeries on odd alternating pretzel knots, and we rule out such surgeries for a large class of Whitehead doubles. Moreover, we rule out cosmetic surgeries for L-space knots along slopes with opposite signs.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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