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  • An intrinsic codimension two cellular decomposition of the Hilbert cube

    Creator:
    Ghimire, Kailash C.
    Abstract:
    Cellular sets in the Hilbert cube are the intersection of nested sequences of normal cubes. One way of getting cellular maps on the Hilbert cube is by decomposing the Hilbert cube into cellular sets and using a quotient map. By using a cellular decomposition of the Hilbert cube, an example...
    Resource Type:
    Dissertation
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    Cellular Decomposition of the Hilbert Cube Abstract approved: Dennis J Garity Cellular sets in the

  • A thin codimension-one decomposition of the Hilbert Cube

    Creator:
    Phon-On, Aniruth
    Abstract:
    For cell-like upper semicontinuous(usc) decompositions G of finite dimensional manifolds M, the decomposition space M/G turns out to be an ANR provided M/G is finite dimensional ([Dav07], page 129 ). Furthermore, if M/G is finite dimensional and has the Disjoint Disks Property (DDP), then M/G is homeomorphic to M ([Dav07],...
    Resource Type:
    Dissertation
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    Abstract approved: Dennis J. Garity For cell-like upper semicontinuous(usc) decompositions G of finite

  • Inequivalent Cantor sets in 𝑅³ whose complements have the same fundamental group

    Creator:
    Garity, Dennis J. and Repovš, Dušan
    Abstract:
    For each Cantor set C in R³, all points of which have bounded local genus, we show that there are infinitely many inequivalent Cantor sets in R³ with the complement having the same fundamental group as the complement of C. This answers a question from Open Problems in Topology and...
    Resource Type:
    Article
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    INEQUIVALENT CANTOR SETS IN R3 WHOSE COMPLEMENTS HAVE THE SAME FUNDAMENTAL GROUP DENNIS J. GARITY AND DUŠAN

  • 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

  • Triangular billiards surfaces and translation covers

    Creator:
    Schmurr, Jason Peter
    Abstract:
    We identify all translation covers among triangular billiards surfaces. Our main tools are the J-invariant of Kenyon and Smillie and a property of triangular billiards surfaces, which we call fingerprint type, that is invariant under balanced translation covers.
    Resource Type:
    Dissertation
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    translation overs among triangular billiards surfa es. Our main toolsare the J-invariant of Kenyon and

  • 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
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    - 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
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    regarded as the group of unit quaternions. Let {1, i, j, k} be the canonical basis of the quaternions

  • 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
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    to thank Dennis Garity for his generous patience and guidance. There are of course many other

  • 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
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    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
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    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