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math.GTJun 11, 2020
7
citations (OpenAlex)
authors
  • András I. Stipsicz
  • Zoltán Szabó
institutions
  • HUN-REN Alfréd Rényi Institute of Mathematics
  • Princeton University
arXiv abstractPDF
paper

Purely cosmetic surgeries and pretzel knots

arXiv:2006.06765 · doi:10.2140/pjm.2021.313.195

Abstract

We show that all pretzel knots satisfy the (purely) cosmetic surgery conjecture, i.e. Dehn surgeries with different slopes along a pretzel knot provide different oriented three-manifolds.

arXiv comment14 pages, 5 figures

References in corpus (9)

  • Holomorphic disks and genus bounds
  • Heegaard Floer homology and alternating knots
  • Cosmetic surgeries on genus one knots
  • On LMO invariant constraints for cosmetic surgery and other surgery problems for knots in S^{3}
  • Surgery formulae for finite type invariants of rational homology 3--spheres
  • Connected sums of knots do not admit purely cosmetic surgeries
  • Two-bridge knots admit no purely cosmetic surgeries
  • 3-braid knots do not admit purely cosmetic surgeries
  • Alternating odd pretzel knots and chirally cosmetic surgeries

Cited by in corpus (2)

  • On constraints for knots to admit chirally cosmetic surgeries and their calculations
  • Twisted Mazur pattern satellite knots and bordered Floer theory
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