Algebraic & Geometric Topology

Least dilatation of pure surface braids

Marissa Loving

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Abstract

We study the minimal dilatation of pseudo-Anosov pure surface braids and provide upper and lower bounds as a function of genus and the number of punctures. For a fixed number of punctures, these bounds tend to infinity as the genus does. We also bound the dilatation of pseudo-Anosov pure surface braids away from zero and give a constant upper bound in the case of a sufficient number of punctures.

Article information

Source
Algebr. Geom. Topol., Volume 19, Number 2 (2019), 941-964.

Dates
Received: 17 February 2018
Revised: 31 July 2018
Accepted: 13 August 2018
First available in Project Euclid: 19 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.agt/1552960831

Digital Object Identifier
doi:10.2140/agt.2019.19.941

Mathematical Reviews number (MathSciNet)
MR3924180

Zentralblatt MATH identifier
07075117

Subjects
Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Secondary: 20F36: Braid groups; Artin groups 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 30F60: Teichmüller theory [See also 32G15] 37B40: Topological entropy 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 57M07: Topological methods in group theory 57M99: None of the above, but in this section

Keywords
mapping class group pseudo Anosov dilatation stretch factor pure surface braids

Citation

Loving, Marissa. Least dilatation of pure surface braids. Algebr. Geom. Topol. 19 (2019), no. 2, 941--964. doi:10.2140/agt.2019.19.941. https://projecteuclid.org/euclid.agt/1552960831


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