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Derived arithmetic Fuchsian groups of genus two. (English) Zbl 1184.11015

The author classifies all cocompact torsion-free derived arithmetic Fuchsian groups of genus two by commensurability classes and shows that there exist no such groups arising from quaternion algebras over number fields of degree greater than five. Also, she proves some results on the existence and form of maximal orders for a class of quaternion algebras related to these groups.

MSC:

11F06 Structure of modular groups and generalizations; arithmetic groups
11R52 Quaternion and other division algebras: arithmetic, zeta functions
20H10 Fuchsian groups and their generalizations (group-theoretic aspects)
57M50 General geometric structures on low-dimensional manifolds
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