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, I. (2018). Rational discrete first degree cohomology for totally disconnected locally compact groups. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 168(2), 361-377 [10.1017/S0305004118000762].

Rational discrete first degree cohomology for totally disconnected locally compact groups

Castellano, I
2018

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)
Articolo in rivista - Articolo scientifico
totally disconnected locally compact groups, cohomology, stallings, ends
English
12-ott-2018
2018
168
2
361
377
open
Castellano, I. (2018). Rational discrete first degree cohomology for totally disconnected locally compact groups. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 168(2), 361-377 [10.1017/S0305004118000762].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/231594
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