Benjamini-Schramm convergence of arithmetic orbifolds.
Duration: 1 hour 13 mins
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| Description: |
Fraczyk, M (Université Paris-Sud 11)
Wednesday 19th April 2017 - 10:00 to 11:00 |
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| Created: | 2017-04-20 17:15 |
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| Collection: | Non-Positive Curvature Group Actions and Cohomology |
| Publisher: | Isaac Newton Institute |
| Copyright: | Fraczyk, M |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Let X be the a symmetric space. We say that a sequence of locally symmetric spaces Benjamini-Schramm converges to X if for any real number R the fraction of the volume taken by the R-thin part tends to 0. In my thesis I showed that for a cocompact, congruence arithmetic hyperbolic 3-manifold the volume of the R-thin part is less than a power less than one of the total volume. As a consequence, any sequence of such manifolds Benjamini-Schramm converges to hyperbolic 3-space. I will give some topological applications of this result. Lastly, I will discuss Benjamini-Schramm convergence of congruence arithmetic orbifolds covered by the symmetric spaces of real rank 1. (joint work with Jean Raimbault).
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