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...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
May 2025
|
| In: |
Mathematische Annalen
Year: 2025, Jahrgang: 392, Heft: 1, Pages: 933-964 |
| ISSN: | 1432-1807 |
| DOI: | 10.1007/s00208-025-03116-7 |
| Online-Zugang: | 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 
|
| Verfasserangaben: | Ilaria Castellano, Bianca Marchionna, Thomas Weigel |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1934696978 | ||
| 003 | DE-627 | ||
| 005 | 20250913141910.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 250826s2025 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s00208-025-03116-7 |2 doi | |
| 035 | |a (DE-627)1934696978 | ||
| 035 | |a (DE-599)KXP1934696978 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Castellano, Ilaria |e VerfasserIn |0 (DE-588)1348300809 |0 (DE-627)1908549858 |4 aut | |
| 245 | 1 | 0 | |a Unimodular totally disconnected locally compact groups of rational discrete cohomological dimension one |c Ilaria Castellano, Bianca Marchionna, Thomas Weigel |
| 264 | 1 | |c May 2025 | |
| 300 | |a 32 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Gesehen am 26.08.2025 | ||
| 500 | |a Online veröffentlicht am 25. Februar 2025 | ||
| 520 | |a 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). | ||
| 650 | 4 | |a 20J05 | |
| 650 | 4 | |a 20J06 | |
| 650 | 4 | |a 22D05 | |
| 700 | 1 | |a Marchionna, Bianca |e VerfasserIn |0 (DE-588)1358585687 |0 (DE-627)1919048596 |4 aut | |
| 700 | 1 | |a Weigel, Thomas |e VerfasserIn |0 (DE-588)1082219401 |0 (DE-627)847205703 |0 (DE-576)455200769 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Mathematische Annalen |d Berlin : Springer, 1869 |g 392(2025), 1 vom: Mai, Seite 933-964 |h Online-Ressource |w (DE-627)254630715 |w (DE-600)1462120-4 |w (DE-576)074529668 |x 1432-1807 |7 nnas |a Unimodular totally disconnected locally compact groups of rational discrete cohomological dimension one |
| 773 | 1 | 8 | |g volume:392 |g year:2025 |g number:1 |g month:05 |g pages:933-964 |g extent:32 |a Unimodular totally disconnected locally compact groups of rational discrete cohomological dimension one |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00208-025-03116-7 |x Verlag |x Resolving-System |z kostenfrei |3 Volltext |
| 856 | 4 | 0 | |u https://https://link.springer.com/article/10.1007/s00208-025-03116-7 |x Verlag |z lizenzpflichtig |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20250826 | ||
| 993 | |a Article | ||
| 994 | |a 2025 | ||
| 998 | |g 1358585687 |a Marchionna, Bianca |m 1358585687:Marchionna, Bianca |d 110000 |d 110400 |e 110000PM1358585687 |e 110400PM1358585687 |k 0/110000/ |k 1/110000/110400/ |p 2 | ||
| 999 | |a KXP-PPN1934696978 |e 4764148129 | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"physDesc":[{"extent":"32 S."}],"relHost":[{"id":{"issn":["1432-1807"],"eki":["254630715"],"zdb":["1462120-4"]},"origin":[{"dateIssuedDisp":"1869-","dateIssuedKey":"1869","publisher":"Springer","publisherPlace":"Berlin ; Heidelberg"}],"physDesc":[{"extent":"Online-Ressource"}],"title":[{"title":"Mathematische Annalen","title_sort":"Mathematische Annalen"}],"language":["eng"],"recId":"254630715","type":{"bibl":"periodical","media":"Online-Ressource"},"disp":"Unimodular totally disconnected locally compact groups of rational discrete cohomological dimension oneMathematische Annalen","note":["Gesehen am 02.12.05"],"part":{"issue":"1","pages":"933-964","year":"2025","extent":"32","volume":"392","text":"392(2025), 1 vom: Mai, Seite 933-964"},"pubHistory":["1.1869 -"]}],"origin":[{"dateIssuedKey":"2025","dateIssuedDisp":"May 2025"}],"id":{"doi":["10.1007/s00208-025-03116-7"],"eki":["1934696978"]},"name":{"displayForm":["Ilaria Castellano, Bianca Marchionna, Thomas Weigel"]},"type":{"bibl":"article-journal","media":"Online-Ressource"},"note":["Gesehen am 26.08.2025","Online veröffentlicht am 25. Februar 2025"],"language":["eng"],"recId":"1934696978","title":[{"title":"Unimodular totally disconnected locally compact groups of rational discrete cohomological dimension one","title_sort":"Unimodular totally disconnected locally compact groups of rational discrete cohomological dimension one"}],"person":[{"roleDisplay":"VerfasserIn","display":"Castellano, Ilaria","role":"aut","family":"Castellano","given":"Ilaria"},{"family":"Marchionna","given":"Bianca","display":"Marchionna, Bianca","roleDisplay":"VerfasserIn","role":"aut"},{"given":"Thomas","family":"Weigel","role":"aut","roleDisplay":"VerfasserIn","display":"Weigel, Thomas"}]} | ||
| SRT | |a CASTELLANOUNIMODULAR2025 | ||