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Showing 1 to 4 of 4 for “"Mapping classes"”.
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Dynamics of free group automorphisms and a subgroup alternative for out(fn)
… of Thurston which states that pseudo- Anosov mapping classes act on the compactified Teichmüller space with north-south dynamics. We prove that several analogues of pseudo-Anosov mapping classes in the Out(F_N) setting act on the space of projective geodesic currents with generalized …
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Least dilatation of pure surface braids
… in the Nielsen-Thurston classification of the mapping class group, a result that is fundamental to the field of low dimensional topology. In particular, Thurston's work gives us a powerful normal form for mapping classes: up to taking powers and restricting to subsurfaces, every mapping class …
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Homology of Configuration Spaces of Surfaces as Mapping Class Group Representations
… of surfaces viewed as representations of the mapping class group of the surface, distinguishing between various flavours: ordered and unordered configurations, of closed surfaces and surfaces with boundary, and with different homology coefficients. In Chapter 2, we prove a version of the …
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Combinatorial models for surface and free group symmetries
… allows combinatorial representation of a surface mapping class group by describing its action on simple closed curves. Similar complexes of spheres, free factors, and free splittings allow combinatorial representation of the automorphisms of a free group. We consider a Birman exact sequence for …