Thesis advisor: Ian Biringer / We consider the space $\rootedH2$ of all complete hyperbolic surfaces without boundary with a basepoint equipped with the pointed Gromov-Hausdorff topology. Continuous paths within $\rootedH2$ arising from certain deformations on a hyperbolic surface and concrete geometric constructions are studied. These include changing some Fenchel-Nielsen parameters of a subsurface, pinching a simple closed geodesic to a cusp, and inserting an infinite strip along a proper bi-infinite geodesic. We then use these paths to show that $\rootedH2$ is path-connected and that it is locally weakly connected at points whose underlying surfaces are either the hyperbolic plane or hyperbolic surfaces of the first kind. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.
Identifer | oai:union.ndltd.org:BOSTON/oai:dlib.bc.edu:bc-ir_109215 |
Date | January 2021 |
Creators | Warakkagun, Sangsan |
Publisher | Boston College |
Source Sets | Boston College |
Language | English |
Detected Language | English |
Type | Text, thesis |
Format | electronic, application/pdf |
Rights | Copyright is held by the author. This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License (http://creativecommons.org/licenses/by-sa/4.0). |
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