Browsing Mathematics (Faculty of) by Subject "topology"
Now showing items 1-4 of 4
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A Fundamentally Topological Perspective on Graph Theory
(University of Waterloo, 2005)We adopt a novel topological approach for graphs, in which edges are modelled as points as opposed to arcs. The model of classical <i>topologized graphs</i> translates graph isomorphism into topological homeomorphism, ... -
Higher Gauge Theory and Discrete Geometry
(University of Waterloo, 2023-06-05)In four dimensions, gravity can be seen as a constrained topological model. This provides a natural way to construct quantum gravity models, since topological models are relatively straightforward to quantize. Difficulty ... -
Self-Dual Graphs
(University of Waterloo, 2002)The study of self-duality has attracted some attention over the past decade. A good deal of research in that time has been done on constructing and classifying all self-dual graphs and in particular polyhedra. We ... -
Trisections of non-orientable 4-manifolds
(University of Waterloo, 2021-08-24)Broadly, this thesis is concerned with trying to understand 4-manifolds through 3-dimensional techniques. From the point of view of smooth manifolds, dimension four is quite unique; one striking illustration of this is the ...