The Volume Flux Group and Nonpositive Curvature
نویسنده
چکیده
We show that a closed nonpositively curved manifold with non-trivial volume flux group has zero minimal volume. It can be seen from the proof that these manifolds admit a finite covering with circle actions whose orbits are homologically essential. LetM be a closed smooth manifold and μ a volume form onM . 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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تاریخ انتشار 2009