Solutions to Two Open Problems in Geometric Group Theory.

[摘要] We introduce a method for analyzing the convex hull of a set in non-positively curved piecewise Euclidean polygonal complexes and we apply this method to prove that with the usual action of F_m x Z^n on the metric product of a tree with R^n, every quasiconvex subgroup of F_m x Z^n is convex.This answers the question whether a quasiconvex subgroup of a CAT(0) group is a CAT(0) group in the affirmative for the groups F_m x Z^n.We also prove bounded packing in a special class of polycyclic groups, and we introduce the notion of coset growth and provide a bound for the coset growth of uniform lattices in Sol.

[发布机构] University of Michigan

[效力级别] Coset Growth

[关键词] Convex Hull;Coset Growth;CAT(0);Polycyclic;Mathematics;Science;Mathematics