Links have no characterising slopes
Geometric Topology
2025-11-27 v1
Abstract
We show that there is no analogue of characterising slopes for multi-component links. Concretely, we show that for any ordered link L in S3 with n>1 components and any rational slopes r_1, ..., r_n, there are infinitely many links L_i with non-homeomorphic complements such that the Dehn fillings L(r_1, ..., r_n) and L_i(r_1, ..., r_n) are homeomorphic.
Cite
@article{arxiv.2511.21506,
title = {Links have no characterising slopes},
author = {Marc Kegel and Misha Schmalian},
journal= {arXiv preprint arXiv:2511.21506},
year = {2025}
}
Comments
10 pages, 13 figures