{"id":"https://openalex.org/W7212127448","doi":"https://doi.org/10.48550/arxiv.2609.10402","title":"A Topological Figiel-Lindenstrauss-Milman Theorem and its Applications","display_name":"A Topological Figiel-Lindenstrauss-Milman Theorem and its Applications","publication_year":2026,"publication_date":"2026-09-09","ids":{"openalex":"https://openalex.org/W7212127448","doi":"https://doi.org/10.48550/arxiv.2609.10402"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.10402","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10402","pdf_url":"https://arxiv.org/pdf/2609.10402","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/2609.10402","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070597025","display_name":"Florian Frick","orcid":"https://orcid.org/0000-0002-7635-744X","observed_orcids":["https://orcid.org/0000-0002-7635-744X"]},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Frick, Florian","raw_affiliation_strings":["Department of Mathematical Sciences , Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031330663","display_name":"Kaave Hosseini","orcid":"https://orcid.org/0000-0002-3497-3500","observed_orcids":["https://orcid.org/0000-0002-3497-3500"]},"institutions":[{"id":"https://openalex.org/I5388228","display_name":"University of Rochester","ror":"https://ror.org/022kthw22","country_code":"US","type":"education","lineage":["https://openalex.org/I5388228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hosseini, Kaave","raw_affiliation_strings":["Department of Computer Science , University of Rochester"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , University of Rochester","institution_ids":["https://openalex.org/I5388228"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114656593","display_name":"Eric Myzelev","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Myzelev, Eric","raw_affiliation_strings":["Department of Mathematical Sciences , Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151227369","display_name":"Arya Narnapatti","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Narnapatti, Arya","raw_affiliation_strings":["Department of Mathematical Sciences , Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5132917776","display_name":"Aliaksei Vasileuski","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vasileuski, Aliaksei","raw_affiliation_strings":["Department of Mathematical Sciences , Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.3237000107765198,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.3237000107765198,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.28130000829696655,"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":0.2556000053882599,"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/free-involutions","display_name":"free involutions","score":0.6890000104904175},{"id":"https://openalex.org/keywords/centrally-symmetric-polytopes","display_name":"centrally symmetric polytopes","score":0.8119999766349792},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"simplicial complexes","score":0.699999988079071},{"id":"https://openalex.org/keywords/real-projective-space","display_name":"real projective space","score":0.7429999709129333},{"id":"https://openalex.org/keywords/triangulation","display_name":"triangulation","score":0.9259999990463257},{"id":"https://openalex.org/keywords/projective-space","display_name":"projective space","score":0.718999981880188},{"id":"https://openalex.org/keywords/torus","display_name":"torus","score":0.7960000038146973},{"id":"https://openalex.org/keywords/symplectic-manifolds","display_name":"symplectic manifolds","score":0.8529999852180481},{"id":"https://openalex.org/keywords/grassmannians","display_name":"Grassmannians","score":0.8999999761581421},{"id":"https://openalex.org/keywords/chromatic-number","display_name":"chromatic number","score":0.7089999914169312},{"id":"https://openalex.org/keywords/vietoris-rips-complex","display_name":"Vietoris-Rips complex","score":0.9869999885559082},{"id":"https://openalex.org/keywords/learning-theory","display_name":"learning theory","score":0.8040000200271606},{"id":"https://openalex.org/keywords/convex-geometry","display_name":"convex geometry","score":0.8999999761581421}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8025000095367432},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6323000192642212},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5805000066757202},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.52920001745224},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.454800009727478},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44130000472068787},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.439300000667572},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.41920000314712524},{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.40139999985694885},{"id":"https://openalex.org/C170315498","wikidata":"https://www.wikidata.org/wiki/Q5282039","display_name":"Discrete Morse theory","level":3,"score":0.3666999936103821},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.3652999997138977},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.36480000615119934},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3440000116825104},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.3292999863624573},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.32409998774528503},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2969000041484833},{"id":"https://openalex.org/C2778478883","wikidata":"https://www.wikidata.org/wiki/Q7825025","display_name":"Topological complexity","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.2840000092983246},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.2680000066757202}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.10402","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10402","pdf_url":"https://arxiv.org/pdf/2609.10402","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.2609.10402","doi":"https://doi.org/10.48550/arxiv.2609.10402","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.10402","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":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.10402","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10402","pdf_url":"https://arxiv.org/pdf/2609.10402","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/G4695586818","display_name":"CAREER: Geometric and Topological Combinatorics","funder_award_id":"2042428","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8051438088","display_name":"Graduate Research Fellowship Program (GRFP)","funder_award_id":"2140739","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212127448.pdf","grobid_xml":"https://content.openalex.org/works/W7212127448.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1963931974","https://openalex.org/W1971361630","https://openalex.org/W2027410459","https://openalex.org/W2028293361","https://openalex.org/W2100437838","https://openalex.org/W2560777309","https://openalex.org/W2761955986","https://openalex.org/W3184086414","https://openalex.org/W3217598447","https://openalex.org/W4293582019","https://openalex.org/W4417422996","https://openalex.org/W7148930015","https://openalex.org/W7165040182"],"related_works":["https://openalex.org/W7223009455","https://openalex.org/W3217598447","https://openalex.org/W4391157500","https://openalex.org/W3083598478","https://openalex.org/W3194206179","https://openalex.org/W2981222727","https://openalex.org/W6922521526","https://openalex.org/W2621989622","https://openalex.org/W6948120253","https://openalex.org/W7128528979"],"abstract_inverted_index":{"We":[0,88],"prove":[1,101],"a":[2,10,31,102],"topological":[3,151],"generalization":[4],"of":[5,13,57],"the":[6,54,97,124],"Figiel--Lindenstrauss--Milman":[7],"inequality,":[8],"answering":[9],"recent":[11],"question":[12],"Frick,":[14],"Hosseini,":[15],"and":[16,30,120,128,135,150,156],"Vasileuski:":[17],"every":[18,66],"nonempty":[19],"strongly":[20],"regular":[21],"CW":[22],"complex":[23,69,119],"with":[24,92],"$v$":[25],"vertices,":[26],"$f$":[27],"maximal":[28],"cells,":[29],"free":[32],"involution":[33],"that":[34,65],"permutes":[35],"its":[36],"cells":[37],"has":[38,75],"$\\mathbb":[39,73],"Z/2$-index":[40],"at":[41,76],"most":[42],"$4\\log":[43],"v\\log":[44],"f$.":[45],"The":[46,81],"classical":[47,115,132],"inequality":[48],"for":[49,113,153],"centrally":[50],"symmetric":[51],"polytopes":[52],"is":[53],"special":[55],"case":[56],"polytope":[58],"boundaries.":[59],"As":[60],"an":[61],"application,":[62],"we":[63,100],"show":[64],"finite":[67],"simplicial":[68],"homotopy":[70],"equivalent":[71],"to":[72],"RP^d$":[74],"least":[77],"$\\exp(\u03a9(\\sqrt":[78],"d))$":[79,94],"vertices.":[80,95],"previous":[82],"best":[83],"lower":[84,111],"bound":[85],"was":[86],"$\u03a9(d^2)$.":[87],"also":[89],"construct":[90],"triangulations":[91],"$\\exp(O(\\sqrt":[93],"Using":[96],"same":[98],"method,":[99],"low-dimensional":[103],"Postnikov":[104],"factorization":[105],"theorem,":[106],"which":[107],"gives":[108],"similar":[109],"vertex":[110],"bounds":[112,152],"several":[114],"families,":[116],"such":[117],"as":[118],"quaternionic":[121],"projective":[122],"spaces,":[123],"$d$-torus,":[125],"closed":[126],"symplectic":[127],"aspherical":[129],"manifolds,":[130],"Grassmannians,":[131],"Lie":[133],"groups,":[134],"spherical":[136],"space":[137],"forms.":[138],"Further":[139],"applications":[140],"include":[141],"results":[142],"in":[143],"learning":[144],"theory,":[145],"convex":[146],"geometry,":[147],"computational":[148],"topology,":[149],"chromatic":[154],"numbers":[155],"Vietoris--Rips":[157],"complexes.":[158]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-11T00:00:00"}
