Bounds on exceptional Dehn filling II

TL;DR

This paper establishes finiteness results for hyperbolic 3-manifolds with many non-hyperbolic Dehn fillings and proves that identifying these manifolds is a decidable problem.

Contribution

It provides new bounds on the number of non-hyperbolic Dehn fillings and shows that classifying such manifolds is algorithmically decidable.

Findings

Finitely many manifolds have more than eight non-hyperbolic Dehn fillings.

Determination of these manifolds is a decidable process.

Abstract

We show that there are at most finitely many one cusped orientable hyperbolic 3-manifolds which have more than eight non-hyperbolic Dehn fillings. Moreover, we show that determining these finitely many manifolds is decidable.