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- W1654492634 abstract "Let $S_n$ be a punctured Riemann spheres $mathbf{S}^2backslash {x_1,..., x_n}$. In this paper, we investigate pseudo-Anosov maps on $S_n$ that are isotopic to the identity on $S_ncup {x_n}$ and have the smallest possible dilatations. We show that those maps cannot be obtained from Thurston's construction (that is the products of two Dehn twists). We also prove that those pseudo-Anosov maps $f$ on $S_n$ with the minimum dilatations can never define a trivial mapping class as any puncture $x_i$ of $S_n$ is filled in. The main tool is to give both lower and upper bounds estimations for dilatations $lambda(f)$ of those pseudo-Anosov maps $f$ on $S_n$ isotopic to the identity as a puncture $x_i$ of $S_n$ is filled in." @default.
- W1654492634 created "2016-06-24" @default.
- W1654492634 creator A5003753515 @default.
- W1654492634 date "2011-05-09" @default.
- W1654492634 modified "2023-09-26" @default.
- W1654492634 title "On pseudo-Anosov maps with small dilatations on punctured Riemann spheres" @default.
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- W1654492634 doi "https://doi.org/10.48550/arxiv.1105.1692" @default.
- W1654492634 hasPublicationYear "2011" @default.
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