Genre
Journal ArticleDate
2012-01-01Author
Futer, DThomas, A
Permanent link to this record
http://hdl.handle.net/20.500.12613/6042
Metadata
Show full item recordDOI
10.1093/imrn/rnr028Abstract
Let Ip,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 Kv,v. We investigate and mostly determine the set of triples (p,v,g) for which there exists a uniform lattice Γ=Γp,v,g in Aut(Ip,v) such that ΓIp,v is a compact orientable surface of genus g. Surprisingly, for some p and g the existence of Γp,v,g depends upon the value of v. The remaining cases lead to open questions in tessellations of surfaces and in number theory. Our construction of Γp,v,g as the fundamental group of a simple complex of groups, together with a theorem of Haglund, implies that for p ≥ 6 every uniform lattice in Aut(I p,v) contains a surface subgroup. We use elementary group theory, combinatorics, algebraic topology, and number theory. © 2011 The Author(s). Published by Oxford University Press. All rights reserved.Citation to related work
Oxford University Press (OUP)Has part
International Mathematics Research NoticesADA compliance
For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.eduae974a485f413a2113503eed53cd6c53
http://dx.doi.org/10.34944/dspace/6024