{"id":"https://openalex.org/W2050753133","doi":"https://doi.org/10.1112/jlms/jdq105","title":"On the Bott periodicity, <i>J</i>-homomorphisms, and <i>H</i> <sub>*</sub> <i>Q</i> <sub>0</sub> <i>S</i> <sup>\u2212<i>k</i> </sup>","display_name":"On the Bott periodicity, <i>J</i>-homomorphisms, and <i>H</i> <sub>*</sub> <i>Q</i> <sub>0</sub> <i>S</i> <sup>\u2212<i>k</i> </sup>","publication_year":2011,"publication_date":"2011-04-22","ids":{"openalex":"https://openalex.org/W2050753133","doi":"https://doi.org/10.1112/jlms/jdq105","mag":"2050753133"},"language":"he","primary_location":{"id":"doi:10.1112/jlms/jdq105","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdq105","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101805875","display_name":"Hadi Zare","orcid":"https://orcid.org/0000-0001-5662-9463"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Hadi Zare","raw_affiliation_strings":["The School of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom"],"affiliations":[{"raw_affiliation_string":"The School of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101805875"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":0.4298,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.56905061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"84","issue":"1","first_page":"204","last_page":"226"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9991000294685364,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9983999729156494,"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/homomorphism","display_name":"Homomorphism","score":0.9390548467636108},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7676306962966919},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7465365529060364},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.7326904535293579},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.593809187412262},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5919787287712097},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5815653800964355},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.475986123085022},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.375460684299469},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3473583161830902},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2931424081325531},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0984930694103241}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.9390548467636108},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7676306962966919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7465365529060364},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.7326904535293579},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.593809187412262},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5919787287712097},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5815653800964355},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.475986123085022},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.375460684299469},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3473583161830902},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2931424081325531},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0984930694103241},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1112/jlms/jdq105","is_oa":false,"landing_page_url":"https://doi.org/10.1112/jlms/jdq105","pdf_url":null,"source":{"id":"https://openalex.org/S4210207695","display_name":"Journal of the London Mathematical Society","issn_l":"0024-6107","issn":["0024-6107","1469-7750"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the London Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1559","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"MIMS Preprint"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1586898120","https://openalex.org/W2017092805","https://openalex.org/W2071196613"],"related_works":["https://openalex.org/W3148895720","https://openalex.org/W2393913406","https://openalex.org/W30258475","https://openalex.org/W4308159138","https://openalex.org/W2356579025","https://openalex.org/W2736697936","https://openalex.org/W3211835374","https://openalex.org/W2548611373","https://openalex.org/W1601809778","https://openalex.org/W2599958490"],"abstract_inverted_index":{"The":[0],"Curtis":[1,70],"conjecture":[2,71],"[Theorem":[3],"7.1,":[4],"Curtis,":[5],"Illinois":[6],"J.":[7,77],"Math.":[8],"19":[9],"(1975)":[10],"231\u2013246]":[11],"predicts":[12],"that":[13,68,108,141],"the":[14,22,27,53,63,69,81,85,104,131,134,145,148,157,170,173],"only":[15],"spherical":[16,117],"classes":[17,118,140],"in":[18,94,119,144,172],"H*(Q0S0;":[19],"\u2124/2)":[20],"are":[21,142],"Hopf":[23],"invariant":[24,29],"one":[25,30],"and":[26,66,84,102],"Kervaire":[28],"elements.":[31],"We":[32,78,123,150],"consider":[33],"Sullivan's":[34],"decomposition":[35],"Q":[36],"0":[37,39],"S":[38],"=":[40,60,113],"J":[41,48,51],"\u00d7":[42],"c":[43],"o":[44],"k":[45],"e":[46],"r":[47],",":[49],"where":[50],"is":[52,99],"fibre":[54],"of":[55,106,133,147,160],"\u03c8q":[56],"\u2212":[57],"1":[58],"(q":[59],"3":[61],"at":[62],"prime":[64],"2)":[65],"observe":[67],"holds":[72],"when":[73,97],"we":[74,115,138,164],"restrict":[75],"to":[76,90],"then":[79],"use":[80],"Bott":[82],"periodicity":[83],"J-homomorphism":[86],"SO":[87],"\u2192":[88],"Q0S0":[89],"define":[91,139],"some":[92,153,167],"generators":[93],"H*(Q0S\u2212k;":[95,128],"\u2124/p),":[96],"p":[98,112],"any":[100],"prime,":[101],"determine":[103,116,124],"type":[105],"subalgebras":[107,126],"they":[109],"generate.":[110],"For":[111],"2":[114],"H*(\u03a9k0":[120],"J;":[121],"\u2124/2).":[122,129,162],"truncated":[125],"inside":[127],"Applying":[130],"machinery":[132],"Eilenberg\u2013Moore":[135],"spectral":[136],"sequence,":[137],"not":[143],"image":[146],"J-homomorphism.":[149],"shall":[151,165],"make":[152,166],"partial":[154],"observations":[155],"on":[156,169],"algebraic":[158],"structure":[159],"H*(\u03a9k0cokerJ;":[161],"Finally,":[163],"comments":[168],"problem":[171],"case":[174],"equivariant":[175],"J-homomorphisms.":[176]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
