{"id":"https://openalex.org/W1999454550","doi":"https://doi.org/10.1007/s10485-007-9071-x","title":"Smash Products for Secondary Homotopy Groups","display_name":"Smash Products for Secondary Homotopy Groups","publication_year":2007,"publication_date":"2007-10-01","ids":{"openalex":"https://openalex.org/W1999454550","doi":"https://doi.org/10.1007/s10485-007-9071-x","mag":"1999454550"},"language":"en","primary_location":{"id":"doi:10.1007/s10485-007-9071-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-007-9071-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10485-007-9071-x.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10485-007-9071-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Hans-Joachim Baues","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Hans-Joachim Baues","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Mathematik, Vivatsgasse 7, 53111, Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Mathematik, Vivatsgasse 7, 53111, Bonn, Germany","institution_ids":["https://openalex.org/I4210119712"]}]},{"author_position":"last","author":{"id":null,"display_name":"Fernando Muro","orcid":null},"institutions":[{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Fernando Muro","raw_affiliation_strings":["Departament d\u2019\u00c0lgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, 08007, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament d\u2019\u00c0lgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, 08007, Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210119712"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.4351,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58138817,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"5","first_page":"551","last_page":"616"},"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":0.9835000038146973,"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":0.9835000038146973,"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":0.00419999985024333,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0034000000450760126,"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/homotopy","display_name":"Homotopy","score":0.7301999926567078},{"id":"https://openalex.org/keywords/homotopy-category","display_name":"Homotopy category","score":0.5383999943733215},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5131999850273132},{"id":"https://openalex.org/keywords/homotopy-group","display_name":"Homotopy group","score":0.47269999980926514},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.43959999084472656},{"id":"https://openalex.org/keywords/higher-category-theory","display_name":"Higher category theory","score":0.4361000061035156},{"id":"https://openalex.org/keywords/n-connected","display_name":"n-connected","score":0.43059998750686646},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4115999937057495}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8377000093460083},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.7301999926567078},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5976999998092651},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.5383999943733215},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5131999850273132},{"id":"https://openalex.org/C147688034","wikidata":"https://www.wikidata.org/wiki/Q1626416","display_name":"Homotopy group","level":3,"score":0.47269999980926514},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.43959999084472656},{"id":"https://openalex.org/C76069219","wikidata":"https://www.wikidata.org/wiki/Q5758318","display_name":"Higher category theory","level":4,"score":0.4361000061035156},{"id":"https://openalex.org/C191752858","wikidata":"https://www.wikidata.org/wiki/Q6358325","display_name":"n-connected","level":3,"score":0.43059998750686646},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4115999937057495},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C35234519","wikidata":"https://www.wikidata.org/wiki/Q3983973","display_name":"Homotopy lifting property","level":4,"score":0.30970001220703125},{"id":"https://openalex.org/C168334404","wikidata":"https://www.wikidata.org/wiki/Q7309601","display_name":"Regular homotopy","level":4,"score":0.29829999804496765},{"id":"https://openalex.org/C150275644","wikidata":"https://www.wikidata.org/wiki/Q1048949","display_name":"Cofibration","level":5,"score":0.29019999504089355},{"id":"https://openalex.org/C131359564","wikidata":"https://www.wikidata.org/wiki/Q1941896","display_name":"Model category","level":4,"score":0.28839999437332153},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C18003601","wikidata":"https://www.wikidata.org/wiki/Q5891833","display_name":"Homotopy sphere","level":4,"score":0.2775000035762787},{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.2759999930858612},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C60394458","wikidata":"https://www.wikidata.org/wiki/Q4948983","display_name":"Bott periodicity theorem","level":5,"score":0.25999999046325684}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10485-007-9071-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-007-9071-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10485-007-9071-x.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0604031","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0604031","pdf_url":"https://arxiv.org/pdf/math/0604031","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:edoc.mpg.de:405946","is_oa":false,"landing_page_url":"http://edoc.mpg.de/405946","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Applied Categorical Structures, v.16, 551-616 (2008)","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10485-007-9071-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10485-007-9071-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10485-007-9071-x.pdf","source":{"id":"https://openalex.org/S148906134","display_name":"Applied Categorical Structures","issn_l":"0927-2852","issn":["0927-2852","1572-9095"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Categorical Structures","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7420919289","display_name":null,"funder_award_id":"FEDER","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1999454550.pdf","grobid_xml":"https://content.openalex.org/works/W1999454550.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1538658958","https://openalex.org/W1584005159","https://openalex.org/W1589880074","https://openalex.org/W1973111660","https://openalex.org/W1980512347","https://openalex.org/W1990094763","https://openalex.org/W2003930372","https://openalex.org/W2062775617","https://openalex.org/W2149618760","https://openalex.org/W3037999612","https://openalex.org/W4254018931","https://openalex.org/W4256304529"],"related_works":[],"abstract_inverted_index":{"We":[0],"construct":[1],"a":[2,14],"smash":[3],"product":[4],"operation":[5],"on":[6,20],"secondary":[7],"homotopy":[8],"groups":[9],"yielding":[10],"the":[11],"structure":[12],"of":[13],"lax":[15],"symmetric":[16],"monoidal":[17],"functor.":[18],"Applications":[19],"cup-one":[21],"products,":[22],"Toda":[23],"brackets":[24],"and":[25],"Whitehead":[26],"products":[27],"are":[28],"considered.":[29]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2016-06-24T00:00:00"}