Publication: Entropy on Riemann Surfaces and the Jacobians of Finite Covers
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Date
2012-11-16
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European Mathematical Society
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McMullen, Curtis T. Forthcoming. Entropy on Riemann surfaces and the Jacobians of finite covers. Commentarii Mathematici Helvetici.
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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.
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