The classification of rank 3 reflective hyperbolic lattices over Z([square root of 2])
| dc.contributor.advisor | Allcock, Daniel, 1969- | en |
| dc.contributor.committeeMember | Reid, Alan | en |
| dc.contributor.committeeMember | Bowen, Lewis | en |
| dc.contributor.committeeMember | Gordon, Cameron | en |
| dc.contributor.committeeMember | Agol, Ian | en |
| dc.creator | Mark, Alice Harway | en |
| dc.creator.orcid | 0000-0001-8823-7456 | en |
| dc.date.accessioned | 2015-10-02T18:15:36Z | en |
| dc.date.accessioned | 2018-01-22T22:28:16Z | |
| dc.date.available | 2015-10-02T18:15:36Z | en |
| dc.date.available | 2018-01-22T22:28:16Z | |
| dc.date.issued | 2015-05 | en |
| dc.date.submitted | May 2015 | en |
| dc.date.updated | 2015-10-02T18:15:37Z | en |
| dc.description | text | en |
| dc.description.abstract | There are 432 strongly squarefree symmetric bilinear forms of signature (2,1) defined over Z([square root of 2]) whose integral isometry groups are generated up to finite index by finitely many reflections. We adapted Allcock's method (based on Nikulin's) of analysis for the 2-dimensional Weyl chamber to the real quadratic setting, and used it to produce a finite list of quadratic forms which contains all of the ones of interest to us as a sub-list. The standard method for determining whether a hyperbolic reflection group is generated up to finite index by reflections is an algorithm of Vinberg. However, for a large number of our quadratic forms the computation time required by Vinberg's algorithm was too long. We invented some alternatives, which we present here. | en |
| dc.description.department | Mathematics | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier | doi:10.15781/T2N300 | en |
| dc.identifier.uri | http://hdl.handle.net/2152/31507 | en |
| dc.language.iso | en | en |
| dc.subject | Hyperbolic reflection groups | en |
| dc.title | The classification of rank 3 reflective hyperbolic lattices over Z([square root of 2]) | en |
| dc.type | Thesis | en |