{"id":"https://openalex.org/W7214005993","doi":"https://doi.org/10.48550/arxiv.2609.24951","title":"Fixed point properties and cohomology of Banach representations of arithmetic groups","display_name":"Fixed point properties and cohomology of Banach representations of arithmetic groups","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214005993","doi":"https://doi.org/10.48550/arxiv.2609.24951"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.24951","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24951","pdf_url":"https://arxiv.org/pdf/2609.24951","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/2609.24951","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152490787","display_name":"Saar Bader","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bader, Saar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020600649","display_name":"Shaked Bader","orcid":"https://orcid.org/0000-0002-9254-3787","observed_orcids":["https://orcid.org/0000-0002-9254-3787"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bader, Shaked","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004257594","display_name":"Uri Bader","orcid":"https://orcid.org/0009-0009-0707-6415","observed_orcids":["https://orcid.org/0009-0009-0707-6415"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bader, Uri","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5112358870","display_name":"Roman Sauer","orcid":"https://orcid.org/0000-0002-2907-6645","observed_orcids":["https://orcid.org/0000-0002-2907-6645"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sauer, Roman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.8330000042915344,"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"}},"topics":[{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.8330000042915344,"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":0.07119999825954437,"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"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.06300000101327896,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fixed-point-theorems","display_name":"fixed point theorems","score":0.9409999847412109},{"id":"https://openalex.org/keywords/arithmetic-groups","display_name":"arithmetic groups","score":0.7139999866485596},{"id":"https://openalex.org/keywords/group-cohomology","display_name":"group cohomology","score":0.8450000286102295},{"id":"https://openalex.org/keywords/vanishing-theorems","display_name":"vanishing theorems","score":0.6830000281333923},{"id":"https://openalex.org/keywords/finite-orbits","display_name":"finite orbits","score":0.8569999933242798},{"id":"https://openalex.org/keywords/gromov-s-conjecture","display_name":"Gromov's conjecture","score":0.9660000205039978},{"id":"https://openalex.org/keywords/symmetric-spaces","display_name":"symmetric spaces","score":0.7599999904632568},{"id":"https://openalex.org/keywords/higher-rank-lattices","display_name":"higher rank lattices","score":0.5910000205039978}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9160000085830688},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.7296000123023987},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5806999802589417},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5716999769210815},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5648000240325928},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.5612999796867371},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5216000080108643},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.42890000343322754},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3885999917984009},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.3815999925136566},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.37619999051094055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3698999881744385},{"id":"https://openalex.org/C131715654","wikidata":"https://www.wikidata.org/wiki/Q288465","display_name":"Group action","level":3,"score":0.3319999873638153},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.321399986743927},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C200681373","wikidata":"https://www.wikidata.org/wiki/Q1260803","display_name":"Rank of an abelian group","level":4,"score":0.2775000035762787},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C155751095","wikidata":"https://www.wikidata.org/wiki/Q1408937","display_name":"Group cohomology","level":3,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.24951","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24951","pdf_url":"https://arxiv.org/pdf/2609.24951","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.2609.24951","doi":"https://doi.org/10.48550/arxiv.2609.24951","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.24951","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:2609.24951","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.24951","pdf_url":"https://arxiv.org/pdf/2609.24951","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":[{"id":"https://openalex.org/G1210808807","display_name":"Isaac Newton Institute for Mathematical Sciences (INI)","funder_award_id":"EP/Z000580/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214005993.pdf","grobid_xml":"https://content.openalex.org/works/W7214005993.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4385848612","https://openalex.org/W4405034967","https://openalex.org/W7106805182"],"related_works":["https://openalex.org/W2283812440","https://openalex.org/W1719047536","https://openalex.org/W1638873192","https://openalex.org/W2076258347","https://openalex.org/W2070155236","https://openalex.org/W4286974759","https://openalex.org/W2000013465","https://openalex.org/W109992120","https://openalex.org/W1522625171","https://openalex.org/W1995541095"],"abstract_inverted_index":{"We":[0,24],"study":[1],"fixed":[2],"point":[3],"theorems":[4],"for":[5,18,27,55],"actions":[6],"of":[7,9,22,32,52,67,97],"lattices":[8,28],"semisimple":[10],"groups.":[11],"They":[12],"are":[13,45],"deduced":[14],"from":[15],"vanishing":[16,54],"results":[17],"the":[19,35,41,53,71,88],"group":[20],"cohomology":[21,36],"$L^p$-representations.":[23],"show":[25],"that":[26,59],"in":[29,78],"simple":[30],"groups":[31],"higher":[33],"rank,":[34],"with":[37],"$L^p$-coefficients":[38],"vanishes":[39],"below":[40,87],"rank":[42,72,89],"whenever":[43],"there":[44],"no":[46],"invariant":[47],"vectors.":[48],"As":[49],"a":[50,74,81,91],"corollary":[51],"$L^1$-coefficients,":[56],"we":[57],"obtain":[58],"every":[60],"action":[61],"on":[62],"an":[63],"acyclic":[64],"simplicial":[65],"complex":[66],"dimension":[68],"lower":[69],"than":[70],"has":[73],"finite":[75],"orbit.":[76],"This":[77],"particular":[79],"proves":[80,90],"conjecture":[82,92],"by":[83,93],"Farb.":[84],"The":[85],"$L^p$-vanishing":[86],"Gromov":[94],"regarding":[95],"$L^p$-cohomology":[96],"symmetric":[98],"spaces.":[99]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}
