Cosmetic surgeries on knots in homology spheres and the Casson--Walker invariant
Kazuhiro Ichihara, In Dae Jong
TL;DR
This paper investigates the conditions under which cosmetic surgeries on knots in homology spheres can occur, utilizing the Casson--Walker invariant to derive new constraints and deepen understanding of such surgeries.
Contribution
It introduces new constraints on knots and surgery slopes for cosmetic surgeries in homology spheres using the rational surgery formula of the Casson--Walker invariant.
Findings
Derived constraints on knots for cosmetic surgeries
Applied Casson--Walker invariant to 2-component links
Enhanced understanding of surgery possibilities in homology spheres
Abstract
We study cosmetic surgeries on a knot in a homology sphere. Several constraints on knots and surgery slopes to admit such surgeries are given. Our main ingredient is the rational surgery formula of the Casson--Walker invariant for 2-component links in the 3-sphere.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Pickering emulsions and particle stabilization · Algebraic Geometry and Number Theory