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Showing 1 to 17 of 17 for “"mapping class group"”.
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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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A computation of the action of the mapping class group on isotopy classes of curves and arcs in surfaces
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1982.
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Visualizing Geometric Structures on Topological Surfaces
… internal measures unchanged. The language of groups gives us a way to distinguish geometric structures. Understanding the mapping class group is an important and hard problem. This paper contributes to visualizing how the mapping class group acts on geometric structures. We explore the …
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The quantum Johnson homomorphism and symplectomorphism of 3-folds
introduce a subset K2,A of the symplectic mapping class group, and an invariant ... that associates a characteristic class in Hochschild cohomology to every symplectomorphism ... K2,A. These are analogues to the familiar Johnson kernel X9 and second Johnson homomorphism - 2 from low-dimensional …
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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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Subgroups of the Torelli group
Let Mod(Sg) be the mapping class group of an orientable surface of genus g, Sg. The action of Mod(Sg) on the homology of Sg induces the well-known symplectic representation: <BR> <BR> <center>Mod(Sg) ---> Sp(2g, Z).</center> <BR> The kernel of this representation is called the Torelli group, I(Sg). …
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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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Two mod-p Johnson filtrations
We consider two mod-p central series of the free group given by Stallings and Zassenhaus. Applying these series to definitions 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 …
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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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Symplectic properties of Milnor fibres
… twists about them generate a free non-abelian subgroup of the symplectic mapping class group. This extends a result of Ishida for Riemann surfaces. The proof generalises the categorical version of Seidel's long exact sequence to arbitrary powers of a fixed Dehn twist. We also show that the Milnor …
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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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Computations in monotone Floer theory
… have infinite order in the symplectic mapping class group; prove that the real projective space split-generates the Fukaya category of the complex projective space and therefore must intersect any other Lagrangian submanifold that is nontrivial in that Fukaya category; and we exhibit a …
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Minimal pseudo-Anosov translation lengths on the Teichmuller space
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-04-19T22:53:25Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 Tsai_Chia-Yen.zip: 561748 bytes, checksum: 33d4032adf3daa4cabdbd93fb0a9fbf0 (MD5) Tsai_Chia-Yen.pdf: 662625 bytes, …
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Generalizations of quasiconvexity for finitely generated groups
For a word-hyperbolic group G, the notion of quasiconvexity of a finitely generated subgroup H of G is independent of the choices of finite generating sets for G and H, and is equivalent to H being quasi- isometrically embedded in G. However, beyond word-hyperbolic groups, the notion of …
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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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Projective twists and the Hopf correspondence
… is the fruit of a research project on a class of symplectic automorphisms called $projective$ $twists$. In the first part of the thesis (Chapters 3,4) we use Picard$-$Lefschetz theory to introduce a new local model for the planar projective twists $\tau_{\mathbb{A}\mathbb{P}^2} \in …
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Combinatorial complexes associated to surfaces
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms