Geometric and Topological Ellipticity in Cohomogeneity Two

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dc.contributor.advisorCohen, Joelen_US
dc.contributor.advisorGrove, Karstenen_US
dc.contributor.authorYeager, Joseph Elwooden_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2012-07-07T05:52:16Z
dc.date.available2012-07-07T05:52:16Z
dc.date.issued2012en_US
dc.description.abstractLet 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.en_US
dc.identifier.urihttp://hdl.handle.net/1903/12662
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledcohomogeneityen_US
dc.subject.pquncontrolledcurvatureen_US
dc.subject.pquncontrolledgroup actionen_US
dc.subject.pquncontrolledorbit spacesen_US
dc.subject.pquncontrolledrational ellipticityen_US
dc.subject.pquncontrolledriemannian manifolden_US
dc.titleGeometric and Topological Ellipticity in Cohomogeneity Twoen_US
dc.typeDissertationen_US

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