Unimodular totally disconnected locally compact groups of rational discrete cohomological dimension one
It is shown that a Stallings-Swan theorem holds in a totally disconnected locally compact (= t.d.l.c.) context (cf. Theorem B). More precisely, a compactly generated $${\mathcal{C}\mathcal{O}}$$-bounded t.d.l.c. group G of rational discrete cohomological dimension less than or equal to 1 must be iso...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
May 2025
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| In: |
Mathematische Annalen
Year: 2025, Volume: 392, Issue: 1, Pages: 933-964 |
| ISSN: | 1432-1807 |
| DOI: | 10.1007/s00208-025-03116-7 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s00208-025-03116-7 Verlag, lizenzpflichtig, Volltext: https://https://link.springer.com/article/10.1007/s00208-025-03116-7 
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| Author Notes: | Ilaria Castellano, Bianca Marchionna, Thomas Weigel |
| Summary: | It is shown that a Stallings-Swan theorem holds in a totally disconnected locally compact (= t.d.l.c.) context (cf. Theorem B). More precisely, a compactly generated $${\mathcal{C}\mathcal{O}}$$-bounded t.d.l.c. group G of rational discrete cohomological dimension less than or equal to 1 must be isomorphic to the fundamental group of a finite graph of profinite groups. This result generalises Dunwoody’s rational version of the classical Stallings-Swan theorem to t.d.l.c. groups. The proof of Theorem B is based on the fact that a compactly generated unimodular t.d.l.c. group with rational discrete cohomological dimension 1 has necessarily non-positive Euler-Poincaré characteristic (cf. Theorem H). |
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| Item Description: | Gesehen am 26.08.2025 Online veröffentlicht am 25. Februar 2025 |
| Physical Description: | Online Resource |
| ISSN: | 1432-1807 |
| DOI: | 10.1007/s00208-025-03116-7 |