Character varieties and harmonic maps to R-trees

Daskalopoulos, Georgios; Dostoglou, Stamatis; Wentworth, Richard

Character varieties and harmonic maps to R-trees

Authors

Daskalopoulos, Georgios

Dostoglou, Stamatis

Wentworth, Richard

Description

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