Links have no characterising slopes

Marc Kegel; Misha Schmalian

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arXiv · 2511.21506

Links have no characterising slopes

Marc Kegel·Misha Schmalian

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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.

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Marc Kegel, Misha Schmalian. 2025-11-26. Links have no characterising slopes. https://arxiv.org/abs/2511.21506

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