POSITIVE TUPLES OF FLAGS, PIECEWISE CIRCULAR WAVEFRONTS, AND THE 3-DIMENSIONAL EINSTEIN UNIVERSE
| dc.contributor.advisor | Zickert, Christian K | en_US |
| dc.contributor.author | Kirk, Ryan Timothy | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2019-09-26T05:34:04Z | |
| dc.date.available | 2019-09-26T05:34:04Z | |
| dc.date.issued | 2019 | en_US |
| dc.description.abstract | Fock and Goncharov defined the notion of positive subsets of a complete flag manifold G/B in order to study higher Teichmüller spaces. In this dissertation, we study the finite positive subsets when G = PSp(4,R) ∼= SO0(3,2). The main tool is the fact that the 3-dimensional Einstein universe, or Lie quadric, is one of the parabolic homogeneous spaces of G and it parametrizes oriented circles in the 2-sphere. We interpret complete flags in this setting as pointed oriented circles in the 2-sphere and the action of G as contactomorphisms of the unit tangent bundle of S2. This leads to an interpretation of positive subsets in G/B in terms of oriented piecewise circular curves in the 2-sphere, or equivalently piecewise linear Legendrian curves in RP3. We parametrize positive triples of flags by a pair of real-valued cross ratios. We explicitly describe a homeomorphism between the configurations space of positive triples of flags and the moduli space of 6-sided, labeled, positive, oriented piecewise circular wavefronts in S2. | en_US |
| dc.identifier | https://doi.org/10.13016/wqxg-bums | |
| dc.identifier.uri | http://hdl.handle.net/1903/24948 | |
| dc.language.iso | en | en_US |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.title | POSITIVE TUPLES OF FLAGS, PIECEWISE CIRCULAR WAVEFRONTS, AND THE 3-DIMENSIONAL EINSTEIN UNIVERSE | en_US |
| dc.type | Dissertation | en_US |
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