Algebraic & Geometric Topology

Hyperbolic graphs of surface groups

Honglin Min

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We give a sufficient condition for the fundamental group of a reglued graph of surfaces to be hyperbolic. A reglued graph of surfaces is constructed by cutting a fixed graph of surfaces along the edge surfaces, then regluing by pseudo-Anosov homeomorphisms of the edge surfaces. By carefully choosing the regluing homeomorphism, we construct an example of such a reglued graph of surfaces, whose fundamental group is not abstractly commensurable to any surface-by-free group, ie which is different from all the examples given by Mosher [Proc. Amer. Math. Soc. 125 (1997) 3447–3455].

Article information

Algebr. Geom. Topol., Volume 11, Number 1 (2011), 449-476.

Received: 14 August 2009
Revised: 14 December 2009
Accepted: 23 October 2010
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F67: Hyperbolic groups and nonpositively curved groups 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 57M07: Topological methods in group theory 20F28: Automorphism groups of groups [See also 20E36]

hyperbolic group pseudo-Anosov homeomorphism commensurable surface-by-free group


Min, Honglin. Hyperbolic graphs of surface groups. Algebr. Geom. Topol. 11 (2011), no. 1, 449--476. doi:10.2140/agt.2011.11.449.

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