Hyperbolic Graphs of Surface Groups

Abstract

We give a sufficient condition under which the fundamental group of a reglued graph of surfaces is 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 commensurate to any surface-by-free group, i.e., which is different from all the examples given in Mosher's paper 'A hyperbolic-by-hyperbolic hyperbolic group'.

52 pages, 7 figures, thesis draft

References in corpus (1)

• Convex cocompact subgroups of mapping class groups

Cited by in corpus (6)

• Convex cocompactness and stability in mapping class groups
• Hyperbolic extensions of free groups
• Stability and the Morse boundary
• Convex cocompactness in mapping class groups via quasiconvexity in right-angled Artin groups
• Regluing graphs of Free Groups
• Pullbacks of metric bundles and Cannon-Thurston maps