Minimal entropy and simplicial volume |
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Authors: | Andrea Sambusetti |
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Institution: | (1) Institut Fourier de Mathématiques, Université de Grenoble 1, BP 74, F-38402 Saint Martin d'Hères, France. E-mail: asambuse@mozart.ujf-grenoble.fr, FR |
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Abstract: | We prove that MinEnt (Y) ∥Y∥ = MinEnt(X) ∥X∥, for manifolds Y whose fundamental group is a subexponential extension of the fundamental group of some negatively curved, locally symmetric
manifold X. This is a particular case of a more general result holding for an arbitrary representation ρ : π1 (Y) →π1 (X), which relates the minimal entropy and the simplicial volume of X to some invariants of the couple (Y, ker (ρ)). Then, we discuss some applications to the minimal volume problem and to Einstein metrics.
Received: 23 December 1998 |
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Keywords: | Mathematics Subject Classification (1991): 53C20-23 53C25-35 54C70 55M25 |
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