2012/12/02 by Lee, Sang Rae · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1212.0257
Hougthon's groups Hn is a family of groups where each Hn consists of `translations at infinity' on n rays of discrete points emanating from the origin on the plane. Brown shows Hn has type FPn-1 but not FPn by constructing infinite dimensional cell complex on which Hn acts with certain conditions. We modify his idea to construct n-dimensional CAT(0) cubical complex Xn on which Hn acts with the same conditions as before. Brown also shows Hn is finitely presented provided n>2. Johnson provides a finite presentation for H3. We extend his result to provide finite presentations of Hn for n>3. We also establish exponential isoperimetric inequalities of Hn for n>2.