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    Veering Triangulations: Theory and Experiment

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    Worden_temple_0225E_13331.pdf
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    TETDEDXregina-tools.py
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    Genre
    Thesis/Dissertation
    Date
    2018
    Author
    Worden, William
    Advisor
    Futer, David
    Committee member
    Stover, Matthew
    Taylor, Samuel J.
    Champanerkar, Abhijit, 1975-
    Department
    Mathematics
    Subject
    Mathematics
    Fibered
    Geometry
    Hyperbolic
    Topology
    Triangulation
    Veering
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/602
    
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    DOI
    http://dx.doi.org/10.34944/dspace/584
    Abstract
    Certain fibered hyperbolic 3-manifolds admit a layered veering triangulation, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. In the first part of this work, we obtain experimental results which shed light on the combinatorial structure of veering triangulations, and its relation to certain topological invariants of the underlying manifold. Among other things, our experimental results strongly suggest that typical veering triangulations are non-geometric, i.e., they cannot be realized as a union of isometrically embedded hyperbolic tetrahedra. In the second part, we prove that veering triangulations are in fact generically non-geometric.
    Description
    Accompanied by two .py files. A Python interpreter is required to run a PY script in Windows.
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