Higher horospherical limit sets for G-modules over CAT(0) spaces
Abstract
The Sigma-invariants of Bieri-Neumann-Strebel and Bieri-Renz involve an action of a discrete group G on a geometrically suitable space M. In the early versions, M was always a finite-dimensional Euclidean space on which G acted by translations. A substantial literature exists on this, connecting the invariants to group theory and to tropical geometry (which, actually, Sigma-theory anticipated). More recently, we have generalized these invariants to the case where M is a proper CAT(0) space on which G acts by isometries. The "0th stage" of this was developed in our paper [BG16]. The present paper provides a higher-dimensional extension of the theory to the "nth stage" for any n.
Cite
@article{arxiv.1712.05480,
title = {Higher horospherical limit sets for G-modules over CAT(0) spaces},
author = {Robert Bieri and Ross Geoghegan},
journal= {arXiv preprint arXiv:1712.05480},
year = {2018}
}
Comments
This replaces a previous version. The introduction has been completely rewritten to make the paper more accessible. Also a couple of minor corrections and insertion of an accidentally omitted proof