Infinitely many geometric triangulations in a cover of every cusped $3$-manifold Meeting link will be posted to topology listserv. Contact Neil Hoffman if you aren't on the listserv, but wish to join the seminar for the day.
Abstract: A triangulation $\mathcal{T}$ of a cusped hyperbolic 3-manifold is geometric if admits a fundamental domain which decomposes into convex ideal tetrahedra with positive angles. It is an open question as to whether every hyperbolic $3$--manifold admits a single geometric triangulation. A follow-up question is how many geometric triangulations can one manifold admit. Dadd and Duan showed that some manifolds admit infinitely many geometric triangulations. And Luo, Schleimer and Tillmann showed that every manifold has a cover admitting at least one geometric triangulation. We prove that every cusped hyperbolic 3–manifold has a finite cover admitting infinitely many geometric ideal triangulations. This cover is constructed in several stages, using tools developed by Gu Ìeritaud, Luo, Schleimer, and Tillmann. The geometric ideal triangulations that we produce can be organized into an infinite binary tree of Pachner moves. This is joint work with Dave Futer.
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