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arXiv · 1712.05480

Higher horospherical limit sets for G-modules over CAT(0) spaces

Robert Bieri·Ross Geoghegan
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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.

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Robert Bieri, Ross Geoghegan. 2017-12-15. Higher horospherical limit sets for G-modules over CAT(0) spaces. https://arxiv.org/abs/1712.05480

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