Surface quotients of hyperbolic buildings

David Futer (Temple University)

Abstract: Bourdon's building is a negatively curved 2-complex built out of hyperbolic right-angled polygons. Its automorphism group is large (uncountable) and remarkably rich. We study, and mostly answer, the question of when there is a discrete subgroup of the automorphism group such that the quotient is a closed surface of genus g. The cases that we treat involve a fun melange of combinatorics, homology theory, and group theory. The cases that are still open quickly lead to open questions in number theory. This is joint work with Anne Thomas.