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 19 of 19 for “"geometric group theory"”.
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Some combinatorial aspects in algebraic topology and geometric group theory
… result is a self-contained dissertation on the theory of the fundamental group and of the coverings. Finally, there are some recent problems in geometric group theory which are related to the presence of finitely presented groups which appear naturally as fundamental groups.
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Nonstandard Methods in Lie Theory
"In this thesis, we apply model theory to Lie theory and geometric group theory. These applications of model theory come via nonstandard analysis. In Lie theory, we use nonstandard methods to prove two results. First, we give a positive solution to the local form of Hilbert's Fifth Problem, which …
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Van Kampen Diagrams and Small Cancellation Theory
… algorithm to determine which words in the free group, F(A), represent the identity in G. In this thesis, we study small cancellation theory, developed by Lyndon, Schupp, and Greendlinger in the mid-1960s, which contributed to the resurgence of geometric group theory. We investigate the …
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Compactness of the space of marked groups and examples of L2-Betti numbers of simple groups
… due to Rostislav Grigorchuk [1], which refers to geometrical group theory and after the first proof I will give a more topological proof. In the second part, our goal is to prove a theorem by Denis Osin and Andreas Thom [2]: for every integer n ≥ 2 and every ε ≥ 0 there exists an infinite simple …
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Graphs Of Free Groups And Their Measure Equivalence.
This work concerns the Geometric Group Theory of an interesting class of groups that can be obtained as graphs of free groups. These groups are called Quadratic Baumslag-Solitar groups, and are defined by graphs of groups that have infinite cyclic edge groups, and whose vertex groups are either …
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Computations and lower bounds for scl and the relative Gromov seminorm
… of stable commutator length, an invariant of groups that measures homological complexity and is connected to several notions of negative curvature in geometric group theory. A first aspect of this is to give exact computations, motivated by questions of rationality. A particular case of …
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Stable subgroups of handlebody groups
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01
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On triangles and quadrilaterals of groups
… the existence of a pair of algebraic and geometric structures on triangles of groups and on quadrilaterals of groups. These structures are an automatic and biautomatic structure. In addition, this paper also discusses the growth function for the quadrilaterals. We show that these groups …
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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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Detecting topological properties of boundaries of hyperbolic groups
In general, a finitely presented group can have very nasty properties, but many of these properties are avoided if the group is assumed to admit a nice action by isometries on a space with a negative curvature property, such as Gromov hyperbolicity. Such groups are surprisingly common: there is a …
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On the Combinatorics of Certain Garside Semigroups
… to the word and conjugacy problems in the braid group on n-strands, using a particular element that he called the fundamental word. Others have since defined fundamental words in the generalized setting of Artin groups, and even more recently in Garside groups. We consider the problem of finding …
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Knot complements and 3-manifolds
The study of 3-manifold groups has reached big success in the last few decades, with the proof of geometrization theorem by Perelman, and several virtually compact special theorems by Wise, etc. In this paper, we will explore several aspects of 3-manifold groups and see what it shows for the knot …
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Discrete and free subgroups of SL₂
In this thesis, we study finitely generated subgroups of the matrix group SL₂ (over various locally compact fields) which are both discrete and free. We first examine the existing literature on two- and three-generated subgroups of SL₂(R) and SL₂(C). Some such subgroups are known to be free, and …
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Separability within alternating groups and randomness
… promotes known residual properties of free groups, surface groups, right angled Coxeter groups and right angled Artin groups to the situation where the quotient is only allowed to be an alternating group. The proofs follow two related threads of ideas. The first thread leads to `alternating' …
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Acylindrical and strong accessibility
… a bound on the number of edges of a graph of groups splitting for when a finitely generated group acts on a tree (𝑘,𝐶)-acylindrically [25]. In the same paper Weidmann conjectures a common generalisation between their result and a theorem of Bestvina and Feighn [2]; which provides a similar …
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Combinatorial models for surface and free group symmetries
… 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 combinatorial …
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Problems and results on linear hypergraphs
… $\circ$ is associative if and only if $A$ is a group multiplication table. Hrushovski asked whether, if $\circ$ is only associative a positive proportion of the time, $A$ must still in some sense be close to a group multiplication table. This problem manifests a well-studied combinatorial theme, …
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Growth of Conjugacy Classes of Reciprocal Words in Triangle Groups
… classes of reciprocal words for triangle groups of the form G = Z2 ∗ H where H is finitely generated and does not contain an order 2 element. We explore cases where H is infinite cyclic and finite cyclic. The quotient O = H/G is an orbifold and contains a cone point of order 2, due to the …
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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