Let Gamma be a non-cocompact lattice on a locally finite regular right-angled building X. Examples of such X include products of locally finite regular or biregular trees, or Bourdon's building I_{p,q}, which has apartments hyperbolic planes tesselated by right-angled p-gons and all vertex links the complete bipartite graph K_{q,q}. We prove that if Gamma has a strict fundamental domain then Gamma is not finitely generated. The proof uses a topological criterion for finite generation and the separation properties of subcomplexes of X called tree-walls. This is joint work with Kevin Wortman (Utah).
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After the seminar we will take the speaker to lunch.
See the Algebra Seminar web page for information about other seminars in the series.
James East james.east@sydney.edu.au
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