Open Access
2011 Hyperbolic graphs of surface groups
Honglin Min
Algebr. Geom. Topol. 11(1): 449-476 (2011). DOI: 10.2140/agt.2011.11.449


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].


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Honglin Min. "Hyperbolic graphs of surface groups." Algebr. Geom. Topol. 11 (1) 449 - 476, 2011.


Received: 14 August 2009; Revised: 14 December 2009; Accepted: 23 October 2010; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1270.20052
MathSciNet: MR2783234
Digital Object Identifier: 10.2140/agt.2011.11.449

Primary: 20F65 , 20F67
Secondary: 20F28 , 57M07

Keywords: commensurable , hyperbolic group , pseudo-Anosov homeomorphism , surface-by-free group

Rights: Copyright © 2011 Mathematical Sciences Publishers

Vol.11 • No. 1 • 2011
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