2024/10/28 by Aliakbar Daemi, Daemi, Aliakbar, Mike Miller Eismeier +3 · 2 citations
Arts and Humanities · #57K30 #57R58 #57R65 #Art, Politics, and Modernism #Biographical and Historical Analysis #FOS: Mathematics #French Literature and Criticism #Geometric Topology (math.GT)
paper · pdf · doi:10.48550/arxiv.2410.21248
openalex publication_date 2024/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The cosmetic surgery conjecture predicts that for a non-trivial knot in the three-sphere, performing two different Dehn surgeries results in distinct oriented three-manifolds. Hanselman reduced the problem to ± 2 or ± 1/n surgeries being the only possible cosmetic surgeries. We remove the case of ± 1/n-surgeries using the Chern-Simons filtration on Floer's original irreducible-only instanton homology, reducing the conjecture to the case of ± 2 surgery on genus 2 knots with trivial Alexander polynomial. We also prove some similar results for surgeries on knots in S2 × S1. As key steps in establishing these results, we define invariants of the oriented homeomorphism type of three-manifolds derived from filtered instanton Floer homology and introduce a new surgery relationship for Floer's instanton homology.