Assouad-Nagata dimension of finitely generated C'(1/6) groups

Levi Sledd

Assouad-Nagata dimension of finitely generated C'(1/6) groups

Group Theory 2020-10-09 v2 Metric Geometry

Authors: Levi Sledd

Abstract

This paper is the first in a two-part series. In this paper, we prove that the Assouad-Nagata dimension of any finitely generated (but not necessarily finitely presented) $C'(1/6)$ group is at most 2. In the next paper, we use this result, along with techniques of classical small cancellation theory, to answer two open questions in the study of asymptotic and Assouad-Nagata dimension of finitely generated groups.

Keywords

assouad-nagata dimension finitely generated groups c'(1/6) groups small cancellation theory asymptotic dimension

Cite

@article{arxiv.1909.06646,
  title  = {Assouad-Nagata dimension of finitely generated C'(1/6) groups},
  author = {Levi Sledd},
  journal= {arXiv preprint arXiv:1909.06646},
  year   = {2020}
}

Comments

20 pages, 10 figures. Some of the results of this paper have now been moved to the sequel paper, "Assouad-Nagata dimension of finitely generated groups and their subgroups."

Assouad-Nagata dimension of finitely generated C'(1/6) groups

Abstract

Keywords

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