Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 13 of 13 for “"Mapping class groups"”.
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Braid groups and mapping class groups for 2-orbifolds
… of this thesis is that pure orbifold braid groups fit into an exact sequence 1$\\rightarrow$ …
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Free products of abelian groups in mapping class groups
… originally come from the study of Kleinian groups. The analogous notion of convex cocompactness for mapping class groups is due to Farb-Mosher. In recent work, Dowdall-Durham-Leininger-Sisto have proposed a definition of “parabolic” geometric finiteness for mapping class groups. In this …
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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 …
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Homological stability of spaces of manifolds via E_k-algebras
… Firstly, we will consider spin mapping class groups of surfaces, and their algebraic analogue —quadratic symplectic groups— using cellular *E<sub>2</sub>*-algebras. We will obtain improvements in their stability results, which for the spin mapping class groups we will show to be …
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Boundaries and hierarchically hyperbolic spaces
… spaces, namely maps from right-angled Artin groups to mapping class groups. We then answer another question of Durham, Hagen, and Sisto, proving that a Teichmuller geodesic ray does not necessarily converge to a unique point in the hierarchically hyperbolic space boundary of Teichmuller …
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Generalizations of quasiconvexity for finitely generated groups
… embedded in G. However, beyond word-hyperbolic groups, the notion of quasiconvexity is not as useful. For a finitely generated group, there are two recent generalizations of the notion of a quasiconvex subgroup of a word-hyperbolic group, a “stable” subgroup and a “Morse” subgroup. Durham and …
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Spaces of diffeomorphisms and embeddings via algebraic K-theory
… paper, presented in Chapter 1, we show that the mapping class group is not an h-cobordism invariant of high-dimensional manifolds by exhibiting h-cobordant manifolds whose mapping class groups have different cardinalities. To do so, we introduce a moduli space of “h-block” bundles and compare it …
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The Asymptotic Cone of Teichmuller Space: Thickness and Divergence
… similar characterizations for right angled Artin groups by Behrstock-Charney and for mapping class groups by Behrstock-Kleiner-Minsky-Mosher. As a corollary of the characterization, we complete the thickness classification of Teichmüller spaces for all surfaces of finite type. In particular, we …
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Two mod-p Johnson filtrations
… of Dennis Johnson's filtration of the mapping class group we obtain two mod-p Johnson filtrations. Further, we adapt the definition of the Johnson homomorphisms to obtain mod-p Johnson homomorphisms. We calculate the image of the first of these homomorphisms. We give generators for the …
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Automorphism Groups of Quadratic Modules and Manifolds
… homological stability for both general linear groups of modules over a ring with finite stable rank and unitary groups of quadratic modules over a ring with finite unitary stable rank. In particular, we do not assume the modules and quadratic modules to be well-behaved in any sense: for …
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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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Least dilatation of pure surface braids
… thesis finds its roots 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, …
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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 …