Index Catalog // ScholarsArchive@OSU

Topological and Dynamical Properties of Cyclically Presented Groups

Creator:: McDermott, Kirk M.
Abstract:: This dissertation investigates the structure and topological properties of cyclicallypresented groups. First, a family of groups called groups of type Z is considered. Withfew exceptions, the finiteness, asphericity, fixed point, and 3-manifold spine problemsare solved. Most groups of type Z have a central element of infinite order fixed by theshift....
Resource Type:: Dissertation
Full Text:: - hematics at Oregon State University, in particular Christine Escher and Dennis Garity, for their important

The cohomology rings of seven dimensional primitive cohomogeneity one manifolds

Creator:: Ultman, Shari K.
Abstract:: A striking feature in the study of Riemannian manifolds of positive sectional curvature is the narrowness of the collection of known examples. In this thesis, we examine the structure of the cohomology rings of three families of compact simply connected seven dimensional Riemannian manifolds that may contain new examples of...
Resource Type:: Dissertation
Full Text:: regarded as the group of unit quaternions. Let {1, i, j, k} be the canonical basis of the quaternions

Mahler's order functions and algebraic approximation of p-adic numbers

Creator:: Dietel, Brian Christopher
Abstract:: If P is an integer polynomial denote the degree of P by ∂(P) and let H(P) be the maximum of the absolute value of the coefficients of P. Define Λ(P)=2[superscript ∂(P)]H(P) and for a fixed prime p let C[subscript p] denote the completion of the algebraic closure of the p-adic...
Resource Type:: Dissertation
Full Text:: committee members, David Finch, Dennis Garity, Thomas Schmidt, Holly Swisher, and Todd Palmer. Personal I

On the Structure of the Orbit Spaces of Almost Torus Manifolds with Non-negative Curvature

Creator:: Dong, Zheting
Abstract:: An almost torus manifold $M$ is a closed $(2n+1)$-dimensional orientable Riemannian manifold with an effective, isometric $n$-torus action such that the fixed point set $M^T$ is non-empty. Almost torus manifolds are analogues of torus manifolds in odd dimension and share many of the characteristics of torus manifolds. For example, both...
Resource Type:: Dissertation

Collision probabilities of convex polygons in spherical two-space

Creator:: Treuden, Mark Richard
Resource Type:: Dissertation

Rigidity of Vertex-Regular Actions on Fuchsian Buildings

Creator:: Smith, Samantha T.
Abstract:: We present a method by which torsion-free groups of automorphisms of a 2-dimensional hyperbolic building which act simply transitively on the vertex set can be constructed, and prove that any such group can be obtained by this construction. The method produces groups defined by finite presentations with strong small cancellation...
Resource Type:: Dissertation
Full Text:: will be called positive if �1 = �2 = · · · = �k = 1. It will be called reduced if x �j ij 6= x−�j+1ij

Classifying seven dimensional manifolds of fixed cohomology type

Creator:: Montagantirud, Pongdate
Abstract:: Finding new examples of compact simply connected spaces admitting a Riemannian metric of positive sectional curvature is a fundamental problem in differential geometry. Likewise, studying topological properties of families of manifolds is very interesting to topologists. The Eschenburg spaces combine both of those interests: they are positively curved Riemannian manifolds...
Resource Type:: Dissertation
Full Text:: them. One year later, in 1982 J. H. Eschenburg [Esb82] was looking for further spaces of positive

A reinterpretation, and new demonstrations of, the Borel Normal Number Theorem

Creator:: Rockwell, Daniel Luke
Abstract:: The notion of a normal number and the Normal Number Theorem date back over 100 years. Émile Borel first stated his Normal Number Theorem in 1909. Despite their seemingly basic nature, normal numbers are still engaging many mathematicians to this day. In this paper, we provide a reinterpretation of the...
Resource Type:: Dissertation
Full Text:: following way: let #N(Bj, b, α) be the number of k, 1 ≤ k ≤ N − j + 1, such that ak+j−1 = bk for 1 ≤ k ≤ j

Notions of complexity in substitution dynamical systems

Creator:: Wing, David Josiah
Abstract:: There has been a lot of work done in recent decades in the field of symbolic dynamics. Much attention has been paid to the so-called "complexity" function, which gives a sense of the rate at which the number of words in the system grow. In this paper, we explore this...
Resource Type:: Dissertation
Full Text:: to thank Dennis Garity for his generous patience and guidance. There are of course many other

Asphericity of length 6 equations over torsion free groups

Creator:: Kim, Seong Kun
Resource Type:: Dissertation

ScholarsArchive@OSU

Topological and Dynamical Properties of Cyclically Presented Groups

The cohomology rings of seven dimensional primitive cohomogeneity one manifolds

Mahler's order functions and algebraic approximation of p-adic numbers

On the Structure of the Orbit Spaces of Almost Torus Manifolds with Non-negative Curvature

Collision probabilities of convex polygons in spherical two-space

Rigidity of Vertex-Regular Actions on Fuchsian Buildings

Classifying seven dimensional manifolds of fixed cohomology type

A reinterpretation, and new demonstrations of, the Borel Normal Number Theorem

Notions of complexity in substitution dynamical systems

Asphericity of length 6 equations over torsion free groups

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