McMullen, Curtis2012-11-162012-11-16McMullen, Curtis T. Forthcoming. Entropy on Riemann surfaces and the Jacobians of finite covers. Commentarii Mathematici Helvetici.0010-25711420-8946http://nrs.harvard.edu/urn-3:HUL.InstRepos:9918807This 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.en-USJournal Article2012-11-1610.4171/CMH/308