{"id":"https://openalex.org/W7213230536","doi":"https://doi.org/10.48550/arxiv.2609.15419","title":"Integral cohomology of classical Artin groups: spherical types $A,C,D$ and affine types $\\widetilde B,\\widetilde C,\\widetilde D$","display_name":"Integral cohomology of classical Artin groups: spherical types $A,C,D$ and affine types $\\widetilde B,\\widetilde C,\\widetilde D$","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213230536","doi":"https://doi.org/10.48550/arxiv.2609.15419"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.15419","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15419","pdf_url":"https://arxiv.org/pdf/2609.15419","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/2609.15419","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151722360","display_name":"F. V. Weinstein","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Weinstein, F. V.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5151722360"],"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":0.8560000061988831,"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":0.8560000061988831,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.1354999989271164,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.002400000113993883,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/artin-groups","display_name":"Artin groups","score":0.9089999794960022},{"id":"https://openalex.org/keywords/integral-cohomology","display_name":"integral cohomology","score":0.9710000157356262},{"id":"https://openalex.org/keywords/braid-groups","display_name":"braid groups","score":0.9490000009536743},{"id":"https://openalex.org/keywords/salvetti-complex","display_name":"Salvetti complex","score":0.7599999904632568},{"id":"https://openalex.org/keywords/generating-series","display_name":"generating series","score":0.5519999861717224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8751000165939331},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6524999737739563},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.5982999801635742},{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.5824999809265137},{"id":"https://openalex.org/C201064014","wikidata":"https://www.wikidata.org/wiki/Q3956993","display_name":"Artin group","level":3,"score":0.5608000159263611},{"id":"https://openalex.org/C33840335","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid group","level":2,"score":0.5440000295639038},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5293999910354614},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3750999867916107},{"id":"https://openalex.org/C178609977","wikidata":"https://www.wikidata.org/wiki/Q3503315","display_name":"Spectral sequence","level":3,"score":0.358599990606308},{"id":"https://openalex.org/C74196217","wikidata":"https://www.wikidata.org/wiki/Q1095535","display_name":"\u010cech cohomology","level":5,"score":0.3483999967575073},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.3212999999523163},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C6128414","wikidata":"https://www.wikidata.org/wiki/Q3892887","display_name":"Affine representation","level":5,"score":0.2994000017642975},{"id":"https://openalex.org/C155751095","wikidata":"https://www.wikidata.org/wiki/Q1408937","display_name":"Group cohomology","level":3,"score":0.29919999837875366},{"id":"https://openalex.org/C140860697","wikidata":"https://www.wikidata.org/wiki/Q5179941","display_name":"Coxeter element","level":3,"score":0.29280000925064087},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29159998893737793},{"id":"https://openalex.org/C147441545","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid theory","level":3,"score":0.2838999927043915},{"id":"https://openalex.org/C62623296","wikidata":"https://www.wikidata.org/wiki/Q686291","display_name":"Affine group","level":3,"score":0.2768999934196472},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C68365058","wikidata":"https://www.wikidata.org/wiki/Q1179446","display_name":"De Rham cohomology","level":4,"score":0.2628999948501587},{"id":"https://openalex.org/C154610627","wikidata":"https://www.wikidata.org/wiki/Q382491","display_name":"Affine plane (incidence geometry)","level":3,"score":0.259799987077713}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.15419","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15419","pdf_url":"https://arxiv.org/pdf/2609.15419","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.2609.15419","doi":"https://doi.org/10.48550/arxiv.2609.15419","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.15419","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.15419","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.15419","pdf_url":"https://arxiv.org/pdf/2609.15419","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213230536.pdf","grobid_xml":"https://content.openalex.org/works/W7213230536.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2114220480"],"related_works":["https://openalex.org/W2018786420","https://openalex.org/W2148784971","https://openalex.org/W1908673079","https://openalex.org/W2069436118","https://openalex.org/W7097052859","https://openalex.org/W7099212289","https://openalex.org/W2621231576","https://openalex.org/W584657790","https://openalex.org/W1664986220","https://openalex.org/W2032213624"],"abstract_inverted_index":{"We":[0,30,93],"determine":[1],"the":[2,6,14,18,23,33,45,50,53,79,101,110],"additive":[3],"structure":[4],"of":[5,13,36,52,58,86,107,109],"integral":[7,34,80,103],"cohomology":[8,35,51,81,104],"groups":[9,16,38,82],"with":[10],"trivial":[11],"coefficients":[12],"Artin":[15],"in":[17,56,65,105],"spherical":[19],"families":[20,25,55],"$A_n,C_n,D_n$":[21],"and":[22,42,76],"affine":[24],"$\\widetilde":[26],"B_n,\\widetilde":[27],"C_n,\\widetilde":[28],"D_n$.":[29],"first":[31],"compute":[32],"braid":[37,111],"by":[39],"algebraic":[40],"methods":[41],"then":[43],"use":[44],"Salvetti":[46],"complexes":[47],"to":[48],"express":[49],"remaining":[54],"terms":[57,106],"these":[59],"computations.":[60],"The":[61],"resulting":[62],"descriptions":[63],"apply":[64],"every":[66],"admissible":[67],"rank.":[68],"For":[69],"each":[70],"family,":[71],"we":[72],"establish":[73],"cohomological":[74],"stabilization":[75],"show":[77],"that":[78,108],"contain":[83],"no":[84],"elements":[85],"order":[87],"$p^2$":[88],"for":[89],"any":[90],"prime":[91],"$p$.":[92],"also":[94],"give":[95],"uniform":[96],"generating":[97],"series":[98],"formulas":[99],"describing":[100],"stable":[102],"groups.":[112]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-16T00:00:00"}
