MCLEOD, JOHN,ANGUS (2013) Arithmetic Hyperbolic Reﬂection Groups. Doctoral thesis, Durham University.
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This thesis uses Vinberg’s algorithm to study arithmetic hyperbolic reﬂection groups which are contained in the groups of units of quadratic forms. We study two families
of quadratic forms: the diagonal forms −dx_0^2 + x_1^2 + ... + x_n^2 ; and the forms whose automorphism groups contain the Bianchi groups. In the ﬁrst instance we classify over Q the pairs (d,n) for which such a group can be found, and in some cases we can compute the volumes of the fundamental polytopes.
In the second instance we use a combination of the geometric and number theoretic information to classify the reﬂective Bianchi groups by ﬁrst classifying the reﬂective extended Bianchi groups, namely the maximal discrete extension of the Bianchi groups in PSL(2,C).
Finally we identify some quadratic forms in the ﬁrst instance and completely classify those in the second which have a quasi-reﬂective structure.
|Item Type:||Thesis (Doctoral)|
|Award:||Doctor of Philosophy|
|Faculty and Department:||Faculty of Science > Mathematical Sciences, Department of|
|Copyright:||Copyright of this thesis is held by the author|
|Deposited On:||15 Aug 2013 12:14|