English

Asymptotic cones of HNN extensions and amalgamated products

Group Theory 2014-10-01 v1

Abstract

Gromov asked whether an asymptotic cone of a finitely generated group was always simply connected or had uncountable fundamental group. We prove that Gromov's dichotomy holds for asympotic cones with cut points, as well as, HNN extensions and amalgamated products where the associated subgroups are nicely embedded. We also show a slightly weaker dichotomy for multiple HNN extensions of free groups.

Keywords

Cite

@article{arxiv.1210.4420,
  title  = {Asymptotic cones of HNN extensions and amalgamated products},
  author = {Curt Kent},
  journal= {arXiv preprint arXiv:1210.4420},
  year   = {2014}
}