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arXiv · 1212.0257

Geometry of Houghton's Groups

Sang Rae Lee
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Abstract

Hougthon's groups H_n is a family of groups where each H_n consists of `translations at infinity' on n rays of discrete points emanating from the origin on the plane. Brown shows H_n has type FP_n-1 but not FP_n by constructing infinite dimensional cell complex on which H_n acts with certain conditions. We modify his idea to construct n-dimensional CAT(0) cubical complex X_n on which H_n acts with the same conditions as before. Brown also shows H_n is finitely presented provided n>2. Johnson provides a finite presentation for H_3. We extend his result to provide finite presentations of H_n for n>3. We also establish exponential isoperimetric inequalities of H_n for n>2.

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Sang Rae Lee. 2012-12-02. Geometry of Houghton's Groups. https://arxiv.org/abs/1212.0257

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