Cosmetic surgeries and the Poincare homology sphere

2019/02/18 by Tye Lidman, Lidman, Tye
Mathematics · Medicine · #Geometric and Algebraic Topology #Historical and Scientific Studies

paper · pdf · doi:10.48550/arxiv.1902.06801

Abstract

In this short note, we prove that if a knot in the Poincare homology sphere is homotopically essential, then it does not admit any purely cosmetic surgeries.

Citations

• CLOSED 3–MANIFOLDS UNCHANGED BY DEHN SURGERY
• Dehn Surgery on Knots

Related

• Cosmetic surgeries on knots in homology spheres and the Casson--Walker invariant
• Thurston norm and cosmetic surgeries
• Cable knots do not admit cosmetic surgeries
• Cosmetic surgeries on knots in S³
• Connected sums of knots do not admit purely cosmetic surgeries