N ov 2 00 8 THE VOLUME FLUX GROUP AND NONPOSITIVE CURVATURE by
نویسنده
چکیده
We show that every closed nonpositively curved manifold with non-trivial volume flux group has zero minimal volume, and admits a finite covering with circle actions whose orbits are homologically essential. This proves a conjecture of Kedra– Kotschick–Morita for this class of manifolds. Let M be a closed smooth manifold and μ a volume form on M . Denote by Diff the group of μ–preserving diffeomorphisms of M , and by Diff 0 its identity component. The μ–flux homomorphism Fluxμ, from the universal covering D̃iff 0 to the (n− 1)–cohomology group H(M ;R), is defined by the formula
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