Search results for "20F28"

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On presentations for mapping class groups of orientable surfaces via Poincaré's Polyhedron theorem and graphs of groups

2021

The mapping class group of an orientable surface with one boundary component, S, is isomorphic to a subgroup of the automorphism group of the fundamental group of S. We call these subgroups algebraic mapping class groups. An algebraic mapping class group acts on a space called ordered Auter space. We apply Poincaré's Polyhedron theorem to this action. We describe a decomposition of ordered Auter space. From these results, we deduce that the algebraic mapping class group of S is a quotient of the fundamental group of a graph of groups with, at most, two vertices and, at most, six edges. Vertex and edge groups of our graph of groups are mapping class groups of orientable surfaces with one, tw…

2010 Mathematics Subject Classification. Primary: 57N0520F05Auter spacepresentationsSecondary: 20F28automorphism groups20F34 Mapping class groups[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR][MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
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Automorphisms of 2–dimensional right-angled Artin groups

2007

We study the outer automorphism group of a right-angled Artin group AA in the case where the defining graph A is connected and triangle-free. We give an algebraic description of Out.AA/ in terms of maximal join subgraphs in A and prove that the Tits’ alternative holds for Out.AA/. We construct an analogue of outer space for Out.AA/ and prove that it is finite dimensional, contractible, and has a proper action of Out.AA/. We show that Out.AA/ has finite virtual cohomological dimension, give upper and lower bounds on this dimension and construct a spine for outer space realizing the most general upper bound. 20F36; 20F65, 20F28

20F36outer spaceCohomological dimensionComputer Science::Digital LibrariesQuantitative Biology::Other01 natural sciencesContractible spaceUpper and lower boundsCombinatorics0103 physical sciences20F650101 mathematicsAlgebraic numberMathematics20F28Quantitative Biology::Biomolecules010102 general mathematicsAstrophysics::Instrumentation and Methods for AstrophysicsOuter automorphism groupAutomorphismGraphArtin groupright-angled Artin groups010307 mathematical physicsGeometry and Topologyouter automorphismsGeometry & Topology
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