UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

More information is available at Theses and Dissertations at University of Maryland Libraries.

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    Geometric and Topological Ellipticity in Cohomogeneity Two
    (2012) Yeager, Joseph Elwood; Cohen, Joel; Grove, Karsten; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Let M be a compact, connected and simply-connected Riemannian manifold, and suppose that G is a compact, connected Lie group acting on M by isometries. The dimension of the space of orbits is called the cohomogeneity of the action. If the direct sum of the higher homotopy groups of M, tensored with the field of rational numbers, is a finite-dimensional vector space over the rationals, then M is said to be rationally elliptic. It is known that M is rationally elliptic if it supports an action of cohomogeneity zero or one. When the cohomogeneity is two, this general result is no longer true. However, we prove that M is rationally elliptic in the two-dimensional case under the added assumption that M has nonnegative sectional curvature.
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    NONNEGATIVELY CURVED FIXED-POINT HOMOGENEOUS MANIFOLDS IN LOW DIMENSIONS
    (2009) Galaz Garcia, Fernando; Grove, Karsten; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    We classify fixed-point homogeneous Riemannian manifolds in dimensions 3 and 4 and determine which nonnegatively curved simply-connected 4-manifolds admit a smooth fixed-point homogeneous circle action with a given orbit space structure.