Description
A Conjecture of Ghys A classical theorem of Jordan states, that any finite group of congruence transformations of an n-dimensional sphere has an abelian subgroup of bounded index. About twenty years ago Etienne Ghys conjectured that the same holds for finite groups of arbitrary continuous transformations of the sphere or, more generally, of any closed manifold. This was proved for many classes of manifolds (e.g. spheres, tori, etc.). Eventually, in 2014 with Balazs Csikos and Laszlo Pyber, we gave counter-examples to it. Then Ghys modified his conjecture: instead of abelian, he asked for a nilpotent subgroup of bounded index. Finally, in 2022 we succeeded in proving the modified conjecture. The proof is an interesting mixture of finite group theory and algebraic topology.