Rational discrete first-degree cohomology for totally disconnected locally compact groups
Rational discrete first-degree cohomology for totally disconnected locally compact groups
It is well known that the existence of more than two ends in the sense of J.R. Stallings for a finitely generated discrete group G can be detected on the cohomology group H1(G,R[G]), where R is either a finite field, the ring of integers or the field of rational numbers. It will be shown (cf. Theorem A*) that for a compactly generated totally disconnected locally compact group G the same information about the number of ends of G in the sense of H. Abels can be provided by dH1(G, Bi(G)), where Bi(G) is the rational discrete standard bimodule of G, and dH•(G, _) denotes rational discrete cohomology as introduced in [6].
As a consequence one has that the class of fundamental groups of a finite graph of profinite groups coincides with the class of compactly presented totally disconnected locally compact groups of rational discrete cohomological dimension at most 1 (cf. Theorem B).
Castellano, Ilaria
4b8a6f84-a6b6-4e27-bf01-a87d921785b7
Castellano, Ilaria
4b8a6f84-a6b6-4e27-bf01-a87d921785b7
Castellano, Ilaria
(2018)
Rational discrete first-degree cohomology for totally disconnected locally compact groups.
Mathematical Proceedings of the Cambridge Philosophical Society.
(doi:10.1017/S0305004118000762).
Abstract
It is well known that the existence of more than two ends in the sense of J.R. Stallings for a finitely generated discrete group G can be detected on the cohomology group H1(G,R[G]), where R is either a finite field, the ring of integers or the field of rational numbers. It will be shown (cf. Theorem A*) that for a compactly generated totally disconnected locally compact group G the same information about the number of ends of G in the sense of H. Abels can be provided by dH1(G, Bi(G)), where Bi(G) is the rational discrete standard bimodule of G, and dH•(G, _) denotes rational discrete cohomology as introduced in [6].
As a consequence one has that the class of fundamental groups of a finite graph of profinite groups coincides with the class of compactly presented totally disconnected locally compact groups of rational discrete cohomological dimension at most 1 (cf. Theorem B).
Text
1506.02310
- Accepted Manuscript
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Submitted date: 2016
Accepted/In Press date: 15 March 2017
e-pub ahead of print date: 12 October 2018
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Local EPrints ID: 412189
URI: http://eprints.soton.ac.uk/id/eprint/412189
ISSN: 0305-0041
PURE UUID: 1bfdd027-8f27-4050-a132-183f54e30df5
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Date deposited: 13 Jul 2017 16:31
Last modified: 15 Mar 2024 15:13
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Author:
Ilaria Castellano
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