Mathematical Research Letters

Volume 5, Issue 4, July 1998 pp. 523-533.

Character varieties and harmonic maps to ${\Bbb R}$-trees

Authors: G. Daskalopoulos, S. Dostoglou, and R. Wentworth
Author institution: Brown University, University of Missouri, and University of California, Irvine

Summary: We show that the Korevaar-Schoen limit of the sequence of equivariant harmonic maps corresponding to a sequence of irreducible $SL_2({\Bbb C})$ representations of the fundamental group of a compact Riemannian manifold is an equivariant harmonic map to an ${\Bbb R}$-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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