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

Part of: Connections with homological algebra and category theory Special aspects of infinite or finite groups

Published online by Cambridge University Press:  12 March 2021

ROBERT BIERI  and
ROSS GEOGHEGAN
ROBERT BIERI
Affiliation:
Robert Bieri, Fachbereich Mathematik, Johann Wolfgang Goethe–Universität Frankfurt, D-60054 Frankfurt am Main, Germany, and Department of Mathematical Sciences, Binghamton University (SUNY), Binghamton, NY 13902-6000, U.S.A. e-mail: [email protected]
ROSS GEOGHEGAN
Affiliation:
Department of Mathematical Sciences, Binghamton University (SUNY), Binghamton, NY 13902-6000, U.S.A. e-mail: [email protected]
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Abstract

The Σ-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, Σ-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 “zeroth 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.

MSC classification

Primary: 20F65: Geometric group theory
Secondary: 20J05: Homological methods in group theory
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 171 , Issue 1 , July 2021 , pp. 133 - 163
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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References

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