Complete exceptional surgeries on two-bridge links

TL;DR

This paper classifies hyperbolic two-bridge links that admit complete exceptional surgeries, identifying all such links and their candidate slopes where surgeries produce non-hyperbolic manifolds while proper sub-fillings remain hyperbolic.

Contribution

It provides a comprehensive list of hyperbolic two-bridge links with complete exceptional surgeries and enumerates all candidate slopes for these surgeries.

Findings

List of all hyperbolic two-bridge links with complete exceptional surgeries.

Enumeration of candidate slopes for these surgeries.

Identification of conditions under which surgeries yield non-hyperbolic manifolds.

Abstract

We give a list of hyperbolic two-bridge links which includes all such links with complete exceptional surgeries, i.e., Dehn surgeries on both components which yield non-hyperbolic manifolds but whose all the proper sub-fillings give hyperbolic manifolds. Also all the candidate slopes of complete exceptional surgeries for them are enumerated in our lists.