# Entropy on Riemann Surfaces and the Jacobians of Finite Covers

 Title: Entropy on Riemann Surfaces and the Jacobians of Finite Covers Author: McMullen, Curtis T. Citation: McMullen, Curtis T. Forthcoming. Entropy on Riemann surfaces and the Jacobians of finite covers. Commentarii Mathematici Helvetici. Full Text & Related Files: entropy_on_riemann_surfaces.pdf (147.0Kb; PDF) Abstract: This paper characterizes those pseudo-Anosov mappings whose entropy can be detected homologically by taking a limit over finite covers. The proof is via complex-analytic methods. The same methods show the natural map $$\mathcal{M}_g \rightarrow \prod \mathcal{A}_h$$, which sends a Riemann surface to the Jacobians of all of its finite covers, is a contraction in most directions. Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:9918807

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