Geodesic
Hyperbolic graphs of surface groups
Min, Honglin1
1Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus OH 43210, USA
Algebraic and Geometric Topology, Tome 11 (2011) no. 1, pp. 449-476
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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].

DOI : 10.2140/agt.2011.11.449
Keywords: hyperbolic group, pseudo-Anosov homeomorphism, commensurable, surface-by-free group

Min, Honglin  1

1 Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus OH 43210, USA 
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Min, Honglin. Hyperbolic graphs of surface groups. Algebraic and Geometric Topology, Tome 11 (2011) no. 1, pp. 449-476. doi: 10.2140/agt.2011.11.449

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