Smith theory, L2 cohomology, isometries of locally symmetric manifolds and moduli spaces of curves

We investigate periodic diffeomorphisms of non-compact aspherical manifolds (and orbifolds) and describe a class of spaces that have no homotopically trivial periodic diffeomorphisms. Prominent examples are moduli spaces of curves and aspherical locally symmetric spaces with non-vanishing Euler characteristic. In the irreducible locally symmetric case, we show that no complete metric has more symmetry than the locally symmetric metric. In the moduli space case, we build on work of Farb and Weinberger and prove an analogue of Royden's theorem for complete finite volume metrics.Comment: 24 page

Contents

finite-volume locally symmetric space

Examples of noncompact nonpositively curved manifolds

We give a simple construction of new, complete, finite volume manifolds of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetric ends of different ranks and their fundamental groups are not duality groups

The action dimension of right‐angled Artin groups

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135257/1/blms0115.pd