Character varieties and harmonic maps to R-trees

Details Character varieties and harmonic maps to R-trees Character varieties and harmonic maps to R-trees

1998-10-06

arxiv.org/abs/math/9810033v1

Mathematics

Differential Geometry

12 pages. Latex. to appear in Math. Res. Lett

Scientific paper

We show that the Korevaar-Schoen limit of the sequence of equivariant harmonic maps corresponding to a sequence of irreducible $SL_2({\mathbb C})$ representations of the fundamental group of a compact Riemannian manifold is an equivariant harmonic map to an ${\mathbb R}$-tree which is minimal and whose length function is projectively equivalent to the Morgan-Shalen limit of the sequence of representations. We then examine the implications of the existence of a harmonic map when the action on the tree fixes an end.

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