Algebraic invariants of hyperbolic 4-orbifolds

Abstract: Given an algebraic subgroup G of the isometry group of hyperbolic n-space $H^n$, one can consider the orbifold $H^n/G$. Hyperbolic 2- and 3-orbifolds are reasonably well-understood; for example, hyperbolic 3-orbifolds correspond to orders of split quaternion algebras and there are algorithms that make use of this structure to compute geometric invariants of the orbifolds such as their volume, numbers of cusps, and fundamental groups. However, already hyperbolic 4-orbifolds belong to untamed wilds. We shall examine this frontier by introducing a class of algebraic groups that have many of the same properties as the Bianchi groups and for which we can compute some geometric invariants of the orbifolds via algebraic invariants of rings with involution.

commutative algebracombinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

UC Davis algebra & discrete math seminar