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Filtering by: Advisor Davies, William A. Remove constraint Advisor: Davies, William A. Committee Member Guo, Ren Remove constraint Committee Member: Guo, Ren

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  • On the Logical Independence of (DR) and (CLA)

    Creator:
    Birnbaum. Dionysus A.
    Abstract:
    In 1941, J.H.C. Whitehead posed the question of whether asphericity is a hereditary property for 2-dimensional CW complexes. This question remains unanswered, but has led to the development of several algebraic and topological properties that are sufficient (but not necessary) for the asphericity of presentation 2-complexes. While many of the...
    Resource Type:
    Dissertation
    Full Text:
    Independence of DR and CLA Abstract approved: William A. Bogley In 1941, J.H.C. Whitehead posed the question

  • A Computational Method for Building Spherical Pictures and Theoretic Results from Explicit Constructions

    Creator:
    Merzenich, Matthias C.
    Abstract:
    Let H be a cyclically-presented group on n generators with a single defining relator. Attempts have been made to classify such groups by their order, their status as a 3-manifold group, and the asphericity status of their presentations. For groups with a defining relator of length 3 these classifications are...
    Resource Type:
    Dissertation
    Full Text:
    Abstract approved: William A. Bogley Let H be a cyclically-presented group on n generators with a single

  • Shift dynamics for cyclically presented groups with length four positive relators

    Creator:
    Parker, Forrest W.
    Abstract:
    In 2014, W. Bogley identified a relation between the algebraic and geometric prop- erties of cyclically presented groups Gn (w) in the case where w = x0xkxl is a positive word of length three. Specifically, it was shown that the dynamics of the shift θG on the group G =...
    Resource Type:
    Dissertation
    Full Text:
    Dynamics for Cyclically Presented Groups with Length Four Positive Relators Abstract approved: William A

  • 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:
    Properties of Cyclically Presented Groups Abstract approved: William A. Bogley This dissertation