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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Lagrangian Representations Of (P, P, P)-Triangle Groups, Paul Wayne Lewis Jr.
Lagrangian Representations Of (P, P, P)-Triangle Groups, Paul Wayne Lewis Jr.
Doctoral Dissertations
We obtain explicit formulae for Lagrangian representations of the (p, q, r)-triangle group into the group of direct isometries of the complex hyperbolic plane in the case where p=q=r. Numerically approximated matrix generators of representations of the (p, p, p)-triangle group are obtained using a special basis. The numerical approximations are then used to guess the exact generators by a process utilizing the LLL algorithm. The matrices are proved rigorously to generate Lagrangian representations of the (p, p, p)-triangle group and are applied to the problem of deciding whether or not an interval contains representations of the (p, p, p)-triangle …
Discrete Geometric Homotopy Theory And Critical Values Of Metric Spaces, Leonard Duane Wilkins
Discrete Geometric Homotopy Theory And Critical Values Of Metric Spaces, Leonard Duane Wilkins
Doctoral Dissertations
Building on the work of Conrad Plaut and Valera Berestovskii regarding uniform spaces and the covering spectrum of Christina Sormani and Guofang Wei developed for geodesic spaces, the author defines and develops discrete homotopy theory for metric spaces, which can be thought of as a discrete analog of classical path-homotopy and covering space theory. Given a metric space, X, this leads to the construction of a collection of covering spaces of X - and corresponding covering groups - parameterized by the positive real numbers, which we call the [epsilon]-covers and the [epsilon]-groups. These covers and groups evolve dynamically as the …
Ultrametric Properties Of Homotopy And Refinement Critical Values, Steven Derochers
Ultrametric Properties Of Homotopy And Refinement Critical Values, Steven Derochers
Chancellor’s Honors Program Projects
No abstract provided.
On The Behavior Of The Asymptotics Of Robertson-Walker Cosmologies As A Function Of The Cosmological Constant, Noah Thomas Schaefferkoetter
On The Behavior Of The Asymptotics Of Robertson-Walker Cosmologies As A Function Of The Cosmological Constant, Noah Thomas Schaefferkoetter
Masters Theses
An analysis of the Einstein Field Equations within a Robertson-Walker Cosmology. More specifically, what values of the cosmological constant will result in a Big Bang.
Bounded Geometry And Property A For Nonmetrizable Coarse Spaces, Jared R Bunn
Bounded Geometry And Property A For Nonmetrizable Coarse Spaces, Jared R Bunn
Doctoral Dissertations
We begin by recalling the notion of a coarse space as defined by John Roe. We show that metrizability of coarse spaces is a coarse invariant. The concepts of bounded geometry, asymptotic dimension, and Guoliang Yu's Property A are investigated in the setting of coarse spaces. In particular, we show that bounded geometry is a coarse invariant, and we give a proof that finite asymptotic dimension implies Property A in this general setting. The notion of a metric approximation is introduced, and a characterization theorem is proved regarding bounded geometry.
Chapter 7 presents a discussion of coarse structures on the …
On The Homology Of Automorphism Groups Of Free Groups., Jonathan Nathan Gray
On The Homology Of Automorphism Groups Of Free Groups., Jonathan Nathan Gray
Doctoral Dissertations
Following the work of Conant and Vogtmann on determining the homology of the group of outer automorphisms of a free group, a new nontrivial class in the rational homology of Outer space is established for the free group of rank eight. The methods started in [8] are heavily exploited and used to create a new graph complex called the space of good chord diagrams. This complex carries with it significant computational advantages in determining possible nontrivial homology classes.
Next, we create a basepointed version of the Lie operad and explore some of it proper- ties. In particular, we prove a …