Representations of some lattices into the group of analytic diffeomorphisms of the sphere S^2

Journal of Singularities
volume 9 (2014), 68-74

Received 30 December 2011. Received in revised form 4 December 2012.

DOI: 10.5427/jsing.2014.9f

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Abstract:

Ghys proved that any morphism from a subgroup of finite index of SL(n, Z) to the group of analytic diffeomorphisms of S^2 has a finite image if n is at least 5. The case n=4 is also claimed to follow along the same arguments; in fact this is not straightforward and that case indeed needs a modification of the argument. In this paper we recall the strategy for n>4 and then focus on the case n=4.

Mathematical Subject Classification:

58D05, 58B25

Author(s) information:

Julie Déserti
Institut de Mathématiques de Jussieu, UMR 7586
Université Paris 7
Bâtiment Sophie Germain, Case 7012
75205 Paris Cedex 13, France
email: deserti@math.jussieu.fr