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

Abstract

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.

24 pages

References in corpus (2)

• Degree theorems and Lipschitz simplicial volume for non-positively curved manifolds of finite volume
• The intrinsic asymmetry and inhomogeneity of Teichmuller space

Cited by in corpus (1)

• Rational manifold models for duality groups