Crossratios, Surface Groups, SL(n,R) and C^{1}(S^1)\rtimes Diff (S^1)

Details Crossratios, Surface Groups, SL(n,R) and C^{1}(S^1)\rtimes Diff (S^1) Crossratios, Surface Groups, SL(n,R) and C^{1}(S^1)\rtimes Diff (S^1)

2005-02-21

arxiv.org/abs/math/0502441v3

Mathematics

Differential Geometry

v2.1 : Theorem 1.3 has been improved. Unnecessary appendix have been removed. Relations between cross ratio and spectrum have

Scientific paper

We present results connecting crossratios, representations of surface groups in $SL(n,\mathbb R)$ and in an infinite dimensional group related to the group of diffeomorphisms of the circle. More precisely, we show that representations of a surface group in $SL(n,\mathbb R)$ can be interpreted as crossratios satisfying specific algebraic relations, and we explain that all these representations sit together in a space of representations with values in the infinite dimensional group $C^{1,h}(S^1)\rtimes Diff^{h}(S^1)$.

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