arXiv subjects

Daniel Groves

Publications and source records attributed to Daniel Groves.

38 records · Page 3Linked to original sources

arXiv2005

Limits of (certain) CAT(0) groups, I: Compactification

The purpose of this paper is to investigate torsion-free groups which act properly and cocompactly on CAT(0) metric spaces which have isolated flats, as defined by Hruska. Our approach is to seek results analogous to those of Sela, Kharlampovich and Miasnikov for free groups and to those of Sela (and Rips and Sela) for torsion-free hyperbolic groups. This paper is the first in a series. In this paper we extract an R-tree from an asymptotic cone of certain CAT(0) spaces. This is analogous to a construction of Paulin, and allows a great deal of algebraic information to be inferred, most of which is left to future work.

math.GR↗

arXiv2004

Limits of (certain) CAT(0) groups, II: The Hopf property and the shortening argument

This is the second in a series of papers about torsion-free groups which act properly and cocompactly on a CAT(0) metric space with isolated flats and relatively thin triangles. Our approach is to adapt the methods of Sela and others for word-hyperbolic groups to this context of non-positive curvature. The main result in this paper is that (under certain technical hypotheses) such a group as above is Hopfian. This (mostly) answers a question of Sela.

math.GR↗