# Kleinian surface groups and filling links

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Speaker:
William Stagner
Affiliation:
Rice University
Date:
Tue, 17/05/2022 - 14:30 - 15:30

Virtual talk.

Freedman and Krushkal recently defined the notion of a filling link in 3-manifolds: a link $$L$$ is filling in $$M$$ if for any 1-spine $$G$$ of $$M$$ which is disjoint from $$L$$, $$\pi_1(G)$$ injects into $$\pi_1(M - L)$$. It turns out that proving the existence of filling links is very subtle, even for concrete examples. In this talk we will investigate an intimate relationship between filling links and Kleinian surface groups. We will leverage this connection to prove the existence of filling links in 3-manifolds of small Heegaard genus, using ideas from minimal surfaces, arithmetic groups, and the Hilden-Lozano-Montesinos theory of universal links.

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