Título: FC-subspaces

Palestrante: Misha Belolipetsky, IMPA
Data: 13/07/2021
Horário: 10:30h
Local: Transmissão online

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Resumo: In a joint work with Nikolay Bogachev, Alexander Kolpakov, and Leone Slavich we discovered an interesting connection between totally geodesic subspaces of a hyperbolic manifold or orbifold and finite subgroups of the commensurator of its fundamental group. We call the totally geodesic subspaces associated to the finite subgroups by fc-subspaces. It appears that these subspaces have some remarkable properties. We show that in an arithmetic orbifold all totally geodesic subspaces are fc and there are infinitely many of them, while in non-arithmetic cases there are only finitely many fc-subspaces and their number is bounded in terms of volume. In the talk, I will discuss these results and if time permits will sketch some other applications of fc-subspaces.