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Showing 1 to 20 of 33 for “"free group"”.
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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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Certain free group functions and untangling closed curves on surfaces
… index functions for finitely generated free groups. In joint work with Ilya Kapovich we obtain lower bounds for these functions and relate these free group results back to the setting of hyperbolic surfaces. Chapters 1-6 in parts comprise of a joint paper with Kapovich that is under …
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Dynamics of free group automorphisms and a subgroup alternative for out(fn)
… we prove several structural theorems for subgroups of Out(F_N).
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Algorithmic and statistical properties of filling elements of a free group, and quantitative residual properties of gamma-limit groups
A filling subgroup of a finitely generated free group F(X) is a subgroup which does not fix a point in any very small action free action on an R-tree. For the free group of rank two, we construct a combinatorial algorithm to determine whether or not a given finitely generated subgroup is filling. …
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On decompositions and Connes's embedding problem of finite von Neumann algebras
… few special classes (e.g. amenable algebras and free group factors). In this dissertation we establish Connes's embedding property for von Neumann algebras satisfying Popa's co-amenability condition. Some decomposition properties of finite von Neumann algebras are also investigated.</p><p>Chapter …
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Generalized Group Presentations and Formal Deformations of Cw Complexes
A Peiffer-Whitehead word system W, or generalized group presentation, consists of generators for a free group and words of various orders n (GREATERTHEQ) 2 representing elements of the free group (n = 2), a free crossed module (n = 3) or a free module (n > 3). The P(,n)-equivalence relation on word …
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Geometric and homological methods in group theory: constructing small group resolutions
Given two groups K and H for which we have the free crossed resolutions, B* --> K and C* --> H respectively. Our aim is to construct a free crossed resolution, A* --> G, by way of induction on the degree n, for any semidirect product G = K x H. First we show how to find a set Z1 of generators for …
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Matrix Representations of Automorphism Groups of Free Groups
… the representation theory of the automorphism group Aut (Fn) of a free group by studying the representation theory of three finite subgroups: two symmetric groups, Sn and Sn+1, and a Coxeter group of type Bn, also known as a hyperoctahedral group. The representation theory of these subgroups is …
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Small intestinal bacterial overgrowth in acute and persistent infantile diarrhoea
… were assigned on an alternate basis to one of 2 groups. One group (carbohydrate-containing group) received a soy-based infant formula containing carbohydrates (Isomil, Ross). The other group (carbohydrate-free group) received an identical milk but from which all carbohydrate had been omitted …
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Van Kampen Diagrams and Small Cancellation Theory
… an 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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Some Results on Free Groups in Combinatorial Group Theory
Let Fm be a free group of a finite rank m ≥ 2. We prove that there exist two elements u 1, u2 ∈ Fm such that every endomorphism y of Fm with non-cyclic image is completely determined by y (u1), y (u2). We obtain this result as a corollary of the construction of a C-test word vn( x1,...,xn), …
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Burnside factors, amenability defects and transitive families of projections in factors of type II(1)
… in the hyperfinite II1 and (ii) a 12 element free transitive family. We then prove that the group von Neumann algebras of the known infinite free Burnside groups are all type II1 factors. Our investigation of weak-amenability properties of Burnside groups leads us to consider the Connes theory …
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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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The effect of directed attention score study procedures on music majors' error detection in three-part instrumental music
… through either visual or aural methods. Visual group participants (n = 20) studied the voice of directed attention (VDA), which was color highlighted, in silence. Aural group participants (n = 20) studied the VDA in a three-phase treatment: sight-singing the VDA, using a piano and their own …
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Dynamics of irreducible endomorphisms of F_n
… non-surjective irreducible endomorphisms of the free group F_n. We show that such an endomorphism \phi is topologically represented by a simplicial immersion f:G \rightarrow G of a marked graph G; along the way we classify the dynamics of \partial \phi acting on \partial F_n: there are at most 2n …
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Properties of Pure Completely Positive Linear Maps of Operator Systems
… + 1)-dimensional operator system spanned in the group C*-algebra C*(Fn) by the n generators of the free group Fn and their inverses, then the identity map in : Sn -> Sn is shown to be a pure completely positive map. Similarly, the identity map jn : NC(n) -> NC(n) on the noncommutative n-cube …
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Operads and Homotopy Theory
In Part I, a notion of a group operad is proposed and then a theory of group operads is developed, extending the classical theories of groups, spaces with actions of groups, covering spaces and classifying spaces of groups. Group operads apply to homotopy theory via their associated monads. As an …
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Some Model Theory of Free Groups
… results, both pertaining to the model theory of free groups. In the first set of results, we prove that non-abelian free groups of finite rank at least 3 or of countable rank are not A-homogeneous. We then build on the proof of this result to show that two classes of groups, namely finitely …
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Computing Interesting Topological Features
… induces an isomorphism between the fundamental groups of both spaces. Since the union of these convex hulls is a polygonal region in the plane, possibly with holes, our result implies that the fundamental group of a planar Rips complex is a free group, allowing us to design efficient algorithms …
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The Hanna Neumann conjecture: A flow detection approach
… Hanna Neumann Conjecture states that if two subgroups of a finitely generated free group have finite ranks m and n, then their intersection has rank N which satisfies $N$ $-$ 1 $\leq$ ($m$ $-$ 1)($n$ $-$ 1). The current work examines this conjecture by restating it in terms of a stronger …
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