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Fully transitive polyhedra with crystallographic symmetry groups
This dissertation sets forth a method for classifying, up to euclidean similarity, fully-transitive polyhedra which have crystallographic symmetry groups. Branko Grunbaum's definition of polyhedron is used, in which the ...
Surface mapping classes and Heegaard decompositions of 3-manifolds
The thesis is constituted in two parts. The first part including the first four chapters concentrates on the surface mapping class groups. The second part including the last three chapters focuses on their applications in ...
Cone manifolds in three-dimensional topology applications to branched covers
Cone manifolds are defined and several standard geometric techniques for Riemannian manifolds are generalized to this setting. Smoothing techniques for approximating cone manifolds by smooth Riemannian manifolds with bounded ...