{"id":"https://openalex.org/W7204914950","doi":"https://doi.org/10.48550/arxiv.2608.30881","title":"Quasi-isometries between graphs of totally disconnected locally compact groups","display_name":"Quasi-isometries between graphs of totally disconnected locally compact groups","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204914950","doi":"https://doi.org/10.48550/arxiv.2608.30881"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30881","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30881","pdf_url":"https://arxiv.org/pdf/2608.30881","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.30881","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119820546","display_name":"Sebastian Giersbach","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Giersbach, Sebastian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5119820546"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.7759000062942505,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.7759000062942505,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.03220000118017197,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.030799999833106995,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quasi-isometry","display_name":"quasi-isometry","score":0.9390000104904175},{"id":"https://openalex.org/keywords/totally-disconnected-locally-compact-groups","display_name":"totally disconnected locally compact groups","score":0.9980000257492065},{"id":"https://openalex.org/keywords/graphs-of-groups","display_name":"graphs of groups","score":0.9480000138282776},{"id":"https://openalex.org/keywords/compactly-generated-groups","display_name":"compactly generated groups","score":0.8870000243186951},{"id":"https://openalex.org/keywords/number-of-ends","display_name":"number of ends","score":0.7760000228881836},{"id":"https://openalex.org/keywords/one-ended-groups","display_name":"one-ended groups","score":0.8920000195503235}],"concepts":[{"id":"https://openalex.org/C89436406","wikidata":"https://www.wikidata.org/wiki/Q1544261","display_name":"Totally disconnected space","level":3,"score":0.8442000150680542},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8216000199317932},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.6875},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6169000267982483},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5985000133514404},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.4546000063419342},{"id":"https://openalex.org/C58450382","wikidata":"https://www.wikidata.org/wiki/Q2147620","display_name":"Locally compact group","level":3,"score":0.4350000023841858},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4219000041484833},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41659998893737793},{"id":"https://openalex.org/C130133044","wikidata":"https://www.wikidata.org/wiki/Q1887083","display_name":"Compact group","level":3,"score":0.41100001335144043},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3481000065803528},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.26759999990463257}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30881","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30881","pdf_url":"https://arxiv.org/pdf/2608.30881","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.30881","doi":"https://doi.org/10.48550/arxiv.2608.30881","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30881","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.30881","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30881","pdf_url":"https://arxiv.org/pdf/2608.30881","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204914950.pdf","grobid_xml":"https://content.openalex.org/works/W7204914950.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7206170546","https://openalex.org/W2952025218","https://openalex.org/W4414761981","https://openalex.org/W2051501496","https://openalex.org/W4388991312","https://openalex.org/W2569482380","https://openalex.org/W2997590568","https://openalex.org/W2338711388","https://openalex.org/W4394668995","https://openalex.org/W4252768692"],"abstract_inverted_index":{"Let":[0],"$G$":[1,54],"and":[2,23,33,51,55,60,70,88],"$H$":[3,56],"be":[4],"compactly":[5,100],"generated":[6,101],"totally":[7],"disconnected":[8],"locally":[9],"compact":[10,32],"(tdlc)":[11],"groups":[12,20,30,36,50],"that":[13,27,53],"decompose":[14],"as":[15],"finite":[16],"graphs":[17],"of":[18,46,68,75,85],"tdlc":[19,49,104],"$(\\mathcal{G},":[21,76],"\\mathcal{A})$":[22,77],"$(\\mathcal{H},":[24,86],"\\mathcal{B})$":[25],"such":[26],"all":[28,34],"edge":[29],"are":[31,57],"vertex":[35,73,83],"have":[37,64],"at":[38],"most":[39],"one":[40],"end.":[41],"We":[42],"generalize":[43],"a":[44,81,107],"result":[45,108],"Papasoglu--Whyte":[47],"to":[48,80],"show":[52],"quasi-isometric":[58,79],"if":[59,62],"only":[61],"they":[63],"the":[65],"same":[66],"number":[67],"ends":[69],"every":[71],"one-ended":[72,82],"group":[74,84],"is":[78],"\\mathcal{B})$,":[87],"vice":[89],"versa.":[90],"As":[91],"an":[92],"application,":[93],"we":[94],"construct":[95],"uncountably":[96],"many":[97],"pairwise":[98],"non-quasi-isometric":[99],"non-discrete":[102],"simple":[103],"groups,":[105],"strengthening":[106],"by":[109],"Smith.":[110]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-02T00:00:00"}
