Hyperbolic graphs of surface groups
Copyright policy )Hyperbolic graphs of surface groups
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
- The Ohio State University United States
20F28, Topological methods in group theory, surface-by-free groups, surface-by-free group, 20F67, pseudo-Anosov homeomorphisms, commensurability, Group Theory (math.GR), 20F65; 20F67, Hyperbolic groups and nonpositively curved groups, graphs of surfaces, commensurable, hyperbolic groups, hyperbolic group, FOS: Mathematics, 57M07, pseudo-Anosov homeomorphism, 20F65, Geometric group theory, Mathematics - Group Theory, Other groups related to topology or analysis, fundamental groups
20F28, Topological methods in group theory, surface-by-free groups, surface-by-free group, 20F67, pseudo-Anosov homeomorphisms, commensurability, Group Theory (math.GR), 20F65; 20F67, Hyperbolic groups and nonpositively curved groups, graphs of surfaces, commensurable, hyperbolic groups, hyperbolic group, FOS: Mathematics, 57M07, pseudo-Anosov homeomorphism, 20F65, Geometric group theory, Mathematics - Group Theory, Other groups related to topology or analysis, fundamental groups
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