{"id":"https://openalex.org/W7222500002","doi":"https://doi.org/10.48550/arxiv.2610.20688","title":"The real Betti realization of very effective Hermitian K-theory","display_name":"The real Betti realization of very effective Hermitian K-theory","publication_year":2026,"publication_date":"2026-10-14","ids":{"openalex":"https://openalex.org/W7222500002","doi":"https://doi.org/10.48550/arxiv.2610.20688"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.20688","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20688","pdf_url":"https://arxiv.org/pdf/2610.20688","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/2610.20688","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093211859","display_name":"Julie Bannwart","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bannwart, Julie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5093211859"],"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9984999895095825,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.000699999975040555,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.00019999999494757503,"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/motivic-spectra","display_name":"motivic spectra","score":0.8069999814033508},{"id":"https://openalex.org/keywords/hermitian-k-theory","display_name":"Hermitian K-theory","score":0.8759999871253967},{"id":"https://openalex.org/keywords/ko-theory","display_name":"KO-theory","score":0.5619999766349792},{"id":"https://openalex.org/keywords/motivic-cohomology","display_name":"motivic cohomology","score":0.8970000147819519},{"id":"https://openalex.org/keywords/algebraic-k-theory","display_name":"algebraic K-theory","score":0.7960000038146973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7620999813079834},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.7312999963760376},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.6855999827384949},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6398000121116638},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.595300018787384},{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.5412999987602234},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.47209998965263367},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4471000134944916},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4077000021934509},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4011000096797943},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3912999927997589},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.36970001459121704},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.34389999508857727},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3366999924182892},{"id":"https://openalex.org/C84254916","wikidata":"https://www.wikidata.org/wiki/Q2981889","display_name":"Motivic cohomology","level":5,"score":0.3337000012397766},{"id":"https://openalex.org/C6778880","wikidata":"https://www.wikidata.org/wiki/Q320245","display_name":"Derived functor","level":3,"score":0.3215999901294708},{"id":"https://openalex.org/C2779185822","wikidata":"https://www.wikidata.org/wiki/Q5141399","display_name":"Cohomology ring","level":4,"score":0.3165000081062317},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31439998745918274},{"id":"https://openalex.org/C145054310","wikidata":"https://www.wikidata.org/wiki/Q212803","display_name":"Algebraic topology","level":3,"score":0.2858000099658966},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C155996607","wikidata":"https://www.wikidata.org/wiki/Q381725","display_name":"Exact functor","level":3,"score":0.25189998745918274}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.20688","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20688","pdf_url":"https://arxiv.org/pdf/2610.20688","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.2610.20688","doi":"https://doi.org/10.48550/arxiv.2610.20688","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.20688","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:2610.20688","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.20688","pdf_url":"https://arxiv.org/pdf/2610.20688","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/G5846448348","display_name":null,"funder_award_id":"TRR 326","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8483945739","display_name":"TRR 326: Geometrie und Arithmetik uniformisierter Strukturen (GAUS)","funder_award_id":"444845124","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222500002.pdf","grobid_xml":"https://content.openalex.org/works/W7222500002.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4417516655","https://openalex.org/W2771354996","https://openalex.org/W4417539002","https://openalex.org/W3104124229","https://openalex.org/W2015356281","https://openalex.org/W2972137761","https://openalex.org/W4414858268","https://openalex.org/W7019368969","https://openalex.org/W1670001998","https://openalex.org/W1532042199"],"abstract_inverted_index":{"Real":[0],"Betti":[1],"realization":[2,46,83],"is":[3],"a":[4,25],"symmetric":[5],"monoidal":[6],"functor":[7,21],"from":[8],"the":[9,20,29,40,44,49,69,76,81,94,98],"category":[10],"of":[11,16,31,47,53,73,84,103],"motivic":[12,86,89],"spectra":[13],"to":[14,24,66],"that":[15,22],"topological":[17],"spectra,":[18],"extending":[19],"associates":[23],"scheme":[26],"over":[27],"$\\mathbb{R}$":[28],"space":[30],"its":[32],"real":[33,45,82],"points.":[34],"In":[35],"this":[36],"article,":[37],"we":[38,78],"identify":[39],"$\\mathcal{E}_1$-ring":[41],"structure":[42],"on":[43],"$\\mathsf{ko}$,":[48],"very":[50,99],"effective":[51,100],"cover":[52,101],"Hermitian":[54],"K-theory":[55,105],"$\\mathsf{KO}$,":[56,97],"by":[57],"an":[58],"explicit":[59],"2-local":[60],"fracture":[61],"square,":[62],"as":[63],"being":[64],"equivalent":[65],"$\\mathsf{L}(\\mathbb{R})_{\\geq":[67],"0}$,":[68],"connective":[70],"L-theory":[71],"spectrum":[72],"$\\mathbb{R}$.":[74],"Along":[75],"way,":[77],"also":[79],"compute":[80],"other":[85],"ring":[87],"spectra:":[88],"cohomology":[90],"$\\mathsf{H}\\mathbb{Z}$":[91],"and":[92],"$\\mathsf{H}\\mathbb{Z}/2$,":[93],"variant":[95],"$\\widetilde{\\mathsf{H}\\mathbb{Z}}$,":[96],"$\\mathsf{kgl}$":[102],"algebraic":[104],"$\\mathsf{KGL}$.":[106]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-17T00:00:00"}
