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December 2005 Braids and Nielsen-Thurston Types of Automorphisms of Punctured Surfaces
Kazuhiro ICHIHARA, Kimihiko MOTEGI
Tokyo J. Math. 28(2): 527-538 (December 2005). DOI: 10.3836/tjm/1244208205

Abstract

Let $F$ be a compact, orientable surface with negative Euler characteristic, and let $x_1, \cdots, x_n$ be $n$ fixed but arbitrarily chosen points on $\mathrm{int}F$, each of which has a (small) diskal neighborhood $D_i \subset F$. Denote by $\mathcal{S}_n(F)$ a subgroup of $\mathrm{Diff}(F)$ consisting of "sliding" maps $f$ each of which satisfies

(1) $f(\{x_1, \dots , x_n\}) = \{x_1, \dots , x_n\}, f(D_1\cup \cdots \cup D_n) = D_1 \cup \cdots \cup D_n $ and

(2) $f$ is isotopic to the identity map on $F$

Then by restricting such automorphisms to $\hat{F} = F - \mathrm{int}(D_1 \cup \cdots \cup D_n)$, we have automorphisms $\hat{f} : \hat{F} \to \hat{F}$, which form a subgroup $\mathcal{S}_n(\hat{F})$ of $\mathrm{Diff}(\hat{F})$. We give a Nielsen-Thurston classification of elements of $\mathcal{S}_n(\hat{F})$ using braids in $F \times I$ which characterize the elements of $\mathcal{S}_n(\hat{F})$.

Citation

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Kazuhiro ICHIHARA. Kimihiko MOTEGI. "Braids and Nielsen-Thurston Types of Automorphisms of Punctured Surfaces." Tokyo J. Math. 28 (2) 527 - 538, December 2005. https://doi.org/10.3836/tjm/1244208205

Information

Published: December 2005
First available in Project Euclid: 5 June 2009

zbMATH: 1100.37025
MathSciNet: MR2191064
Digital Object Identifier: 10.3836/tjm/1244208205

Subjects:
Primary: 37E30
Secondary: 57M50, 57N10

Rights: Copyright © 2005 Publication Committee for the Tokyo Journal of Mathematics

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Vol.28 • No. 2 • December 2005
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