Dynamics on nilpotent character varieties

Abstract

Let R(N,G) be the connected component of the identity of the variety of representations of a finitely generated nilpotent group N into a connected compact Lie group G, and let X(N,G) be the corresponding moduli space. We show that there exists a natural Out(N)-invariant measure on X(N,G) and that whenever Out(N) has at least one hyperbolic element, the action of Out(N) on X(N,G) is mixing with respect to this measure.

arXiv comment17 pages, Version 2 has minor updates and corrections, accepted for publication in Conformal Geometry and Dynamics

References in corpus (3)

• Cohomology of the space of commuting n-tuples in a compact Lie group
• The mapping class group action on SU(3)-character varieties
• On the Torelli group action on compact character varieties

Cited by in corpus (1)

• Non-ergodicity on SU(2) and SU(3) character varieties of the once-punctured torus