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Filtering by: Committee Member Bogley, William A.

Enumeration Problems on Symmetries of Riemann Surfaces

Creator:

Camacho, Charles A.

Abstract:

We describe two combinatorial problems in the theory of automorphism groups of compact Riemann surfaces of genus two or greater: enumerate the topological actions of a finite group on surfaces and determine the set of genera of surfaces admitting such a group action, called the genus spectrum. We illustrate results...

Resource Type:

Dissertation
On the Topologies of Moduli Spaces of Polygons: A Taxonomic Approach

Creator:

Krughoff, Stephen A.

Abstract:

Consider a polygon lying in the Euclidean plane with labeled edge lengths. The moduli space of polygons is the space of all polygons with the same labeled edge lengths, modulo orientation preserving isometries. It is well known that this space is generically a smooth manifold. For certain combinations of edge...

Resource Type:

Dissertation
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