An arithmetic, hyperbolic, rational homology 3-sphere that bounds geometrically – Leonardo Ferrari (Neuchatel (Svizzera))

Venue

Aula Magna – Dipartimento di Matematica.

Abstract

In this seminar, we’ll introduce Davis and Januszkiewicz combinatorial techniques for building manifolds from right-angled polytope, as well as some topological properties inherited by these manifolds. We’ll then present some obstructions to producing rational homology 3-spheres (QHS3) in this setting, and explain how to use this obstructions to improve tree-search algorithms for hyperbolic QHS3. We’ll finally explain how to promote geodesical embeddings to geometrical bounds, and combine these tools to construct the first example of a hyperbolic, arithmetic, QHS3 that bounds geometrically.

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