Fadi Mezher
| Title: | Arithmeticity of some automorphism groups of high dimensional manifolds |
| Speaker: | Fadi Mezher |
| Time: | Thursday, 15.05.2025, 14:00 |
| Place: | SR 3.69 |
Abstract:
For W a smooth manifold of dimension at least 5, the group of isotopy classes of diffeomorphisms of W (the smooth mapping class group) and the group of isotopy classes of homeomorphisms (the topological mapping class group) of W are classical objects of study in geometric topology. By a combination of surgery theory and rational homotopy theory, Sullivan shows that the above groups are commensurable up to finite kernel to arithmetic groups. Their arithmeticity is therefore equivalent to another classical group theoretic notion, that of residual finiteness. Building on work of Deligne on symplectic groups, and Kervaire–Milnor on exotic spheres, Krannich and Randal-Williams show that the smooth mapping class group need not be residually finite, hence also not arithmetic. In contrast to the smooth setting, we show, using embedding calculus and profinite homotopy theory, that the topological mapping class group is residually finite, and therefore arithmetic. The talk is intended as an overview of the above results.