Dissertation/Thesis Abstract

Geometric and topological ellipticity in cohomogeneity two
by Yeager, Joseph E., Ph.D., University of Maryland, College Park, 2012, 62; 3517839
Abstract (Summary)

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.

Indexing (document details)
Advisor: Cohen, Joel, Grove, Karsten
Commitee: Gates, Sylvester, Halperin, Stephen, Schafer, James
School: University of Maryland, College Park
Department: Mathematics
School Location: United States -- Maryland
Source: DAI-B 73/12(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Cohomogeneity, Curvature, Group action, Orbit spaces, Rational ellipticity, Riemannian manifolds
Publication Number: 3517839
ISBN: 9781267483867
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