2010/07/07 by Thomas Koberda, Koberda, Thomas · 3 citations
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.1007.1118
Consider the mapping class group Modg,p of a surface \Σg,p of\ngenus g with p punctures, and a finite collection f1,...,fk of\nmapping classes, each of which is either a Dehn twist about a simple closed\ncurve or a pseudo-Anosov homeomorphism supported on a connected subsurface. In\nthis paper we prove that for all sufficiently large N, the mapping classes\n f1N,...,fkN generate a right-angled Artin group. The right-angled\nArtin group which they generate can be determined from the combinatorial\ntopology of the mapping classes themselves. When f1,...,fk are\narbitrary mapping classes, we show that sufficiently large powers of these\nmapping classes generate a group which embeds in a right-angled Artin group in\na controlled way. We establish some analogous results for real and complex\nhyperbolic manifolds. We also discuss the unsolvability of the isomorphism\nproblem for finitely generated subgroups of Modg,p, and prove that the\nisomorphism problem for right-angled Artin groups is solvable. We thus\ncharacterize the isomorphism type of many naturally occurring subgroups of\n Modg,p.\n