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

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

2011-06-09

arxiv.org/abs/1106.1704v1

Mathematics

Geometric Topology

24 pages

Scientific paper

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.

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