Surface quotients of hyperbolic buildings

If you wish to join the group going across to UNSW by taxi for Anne's talk, please e-mail me emma.carberry@sydney.edu.au by Thursday evening. We will meet at 12 PM just inside the city Road entrance to Sydney University to catch the taxi, and will meet our colleagues at UNSW under the fig tree outside the red centre at 12:30 PM.

Speaker: Dr. Anne Thomas (University of Sydney)

Title: Surface quotients of hyperbolic buildings

Date: Friday, 5th of November, 2010

Time: 14:00

Venue: Room OMB 145, Old Main Building, UNSW

Abstract:

Let I(p,v) be Bourdon's building, the unique simply-connected 2-complex such that all 2-cells are regular right-angled hyperbolic p-gons and the link at each vertex is the complete bipartite graph K_{v,v}. We investigate and mostly determine the set of triples (p,v,g) for which there is a discrete group acting on I(p,v) so that the quotient is a compact orientable surface of genus g. Surprisingly, the existence of such a quotient depends upon the value of v. The remaining cases lead to open questions in tessellations of surfaces and in number theory. We use elementary group theory, combinatorics, algebraic topology and number theory.

This is joint work with David Futer.