Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 19, Number 2 (2019), 941-964.
Least dilatation of pure surface braids
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.
Algebr. Geom. Topol., Volume 19, Number 2 (2019), 941-964.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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