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Minimal entropy and simplicial volume

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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.

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Received: 23 December 1998

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Sambusetti, A. Minimal entropy and simplicial volume. manuscripta math. 99, 541–560 (1999). https://doi.org/10.1007/s002290050190

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  • DOI: https://doi.org/10.1007/s002290050190

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