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Classification of simply connected cohomogeneity one manifolds in lower dimensions
Muzzy, Sara E.
Muzzy, Sara E.
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2017-05
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Electronic dissertations
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Abstract
A cohomogeneity one manifold is a topological manifold with an effective topological
action of a compact Lie group whose quotient is one dimensional. Cohomogeneity one
manifolds were introduced by Mostert in 1957, however Mostert's original structure theorem
had two omissions. The first omission was corrected by Neumann in 1967 but the second
omission was not corrected until 2015 by Galaz-Garcia and Zarei. In this paper we will examine
the revised structure theorems for cohomogeneity one manifolds and compile all work
done by Parker, Neumann, Mostert, Hoelscher, Galaz-Garcia and Zarei on the equivariant
classification of closed, simply connected cohomogeneity one manifolds in dimensions up to
7.
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Thesis (M.S.)--Wichita State University, Fairmount College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics, and Physics
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Wichita State University
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Copyright 2017 by Sara Elizabeth Muzzy
All Rights Reserved