Fundamental domains for proper affine actions of Coxeter groups in three dimensions
| dc.contributor.advisor | Goldman, William M | en_US |
| dc.contributor.author | Laun, Gregory | 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 | 2016-06-22T06:10:55Z | |
| dc.date.available | 2016-06-22T06:10:55Z | |
| dc.date.issued | 2016 | en_US |
| dc.description.abstract | We study proper actions of groups $G \cong \Z/2\Z \ast \Z/2\Z \ast \Z/2\Z$ on affine space of three real dimensions. Since $G$ is nonsolvable, work of Fried and Goldman implies that it preserves a Lorentzian metric. A subgroup $\Gamma < G$ of index two acts freely, and $\R^3/\Gamma$ is a Margulis spacetime associated to a hyperbolic surface $\Sigma$. When $\Sigma$ is convex cocompact, work of Danciger, Gu{\'e}ritaud, and Kassel shows that the action of $\Gamma$ admits a polyhedral fundamental domain bounded by crooked planes. We consider under what circumstances the action of $G$ also admits a crooked fundamental domain. We show that it is possible to construct actions of $G$ that fail to admit crooked fundamental domains exactly when the extended mapping class group of $\Sigma$ fails to act transitively on the top-dimensional simplices of the arc complex of $\Sigma$. We also provide explicit descriptions of the moduli space of $G$ actions that admit crooked fundamental domains. | en_US |
| dc.identifier | https://doi.org/10.13016/M2WR22 | |
| dc.identifier.uri | http://hdl.handle.net/1903/18362 | |
| dc.language.iso | en | en_US |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.subject.pquncontrolled | Affine Structures | en_US |
| dc.subject.pquncontrolled | Fundamental Domains | en_US |
| dc.subject.pquncontrolled | Margulis Spacetimes | en_US |
| dc.subject.pquncontrolled | Proper Actions | en_US |
| dc.title | Fundamental domains for proper affine actions of Coxeter groups in three dimensions | en_US |
| dc.type | Dissertation | en_US |
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