Hyperbolic graphs of surface groups

Min, Honglin

doi:10.2140/agt.2011.11.449

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Hyperbolic graphs of surface groups

Honglin Min

Algebraic & Geometric Topology 11 (2011) 449–476

DOI: 10.2140/agt.2011.11.449

Abstract

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].

Keywords

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

Mathematical Subject Classification 2000

Primary: 20F67, 20F65

Secondary: 57M07, 20F28

References

Publication

Received: 14 August 2009

Revised: 14 December 2009

Accepted: 23 October 2010

Published: 25 January 2011

Authors

Honglin Min
Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus OH 43210 USA

Volume 11, issue 1 (2011)