Finiteness of purely cosmetic fillings
Geometric Topology
2026-02-04 v1
Abstract
A pair of Dehn fillings on a compact, orientable 3-manifold with a torus boundary is said to be purely cosmetic if the resulting 3-manifolds are orientation-preservingly homeomorphic. In this paper, we show that if the torus boundary is incompressible, then there are only finitely many pairs of purely cosmetic fillings.
Cite
@article{arxiv.2509.03788,
title = {Finiteness of purely cosmetic fillings},
author = {Kazuhiro Ichihara},
journal= {arXiv preprint arXiv:2509.03788},
year = {2026}
}
Comments
7 pages