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arXiv · 2509.03788

Finiteness of purely cosmetic fillings

Kazuhiro Ichihara
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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.

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Kazuhiro Ichihara. 2025-09-04. Finiteness of purely cosmetic fillings. https://doi.org/10.4153/s000843952610174x

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