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Theses

Invariants globaux des variétés hyperboliques quaterioniques

Abstract : In the first part of this thesis, we derive explicit universal – that is, depending only on the dimension – lower bounds on three global invariants of quaternionic hyperbolic sapces : their maximal radius, their volume, and their Euler caracteristic. We also exhibit an upper bound on their Margulis constant, showing that this last quantity decreases at least like a negative power of the dimension. In the second part, we study a specific lattice of isometries of the quaternionic hyperbolic plane : the Hurwitz modular group. In particular, we show that this group is generated by four elements, and we construct a fundamental domain for the subgroup of isometries of this lattice stabilising a point on the boundary of the quaternionic hyperbolic plane.
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Zoe Philippe. Invariants globaux des variétés hyperboliques quaterioniques. Mathématiques générales [math.GM]. Université de Bordeaux, 2016. Français. ⟨NNT : 2016BORD0453⟩. ⟨tel-01661448⟩

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