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- W3106403092 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 exists a uniform lattice {Gamma} in Aut(I(p,v)) such that {Gamma}I(p,v) is a compact orientable surface of genus g. Surprisingly, the existence of {Gamma} depends upon the value of v. The remaining cases lead to open questions in tessellations of surfaces and in number theory. Our construction of {Gamma}, together with a theorem of Haglund, implies that for p>=6, every uniform lattice in Aut(I) contains a surface subgroup. We use elementary group theory, combinatorics, algebraic topology, and number theory." @default.
- W3106403092 created "2020-11-23" @default.
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- W3106403092 date "2011-03-16" @default.
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- W3106403092 title "Surface Quotients of Hyperbolic Buildings" @default.
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- W3106403092 doi "https://doi.org/10.1093/imrn/rnr028" @default.
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