{"id":"https://openalex.org/W1993673539","doi":"https://doi.org/10.1090/s0002-9947-1985-0768729-x","title":"Bounded Homotopy Equivalences of Hilbert Cube Manifolds","display_name":"Bounded Homotopy Equivalences of Hilbert Cube Manifolds","publication_year":1985,"publication_date":"1985-02-01","ids":{"openalex":"https://openalex.org/W1993673539","doi":"https://doi.org/10.1090/s0002-9947-1985-0768729-x","mag":"1993673539"},"language":"en","primary_location":{"id":"doi:10.1090/s0002-9947-1985-0768729-x","doi":"https://doi.org/10.1090/s0002-9947-1985-0768729-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1985-0768729-x","pdf_url":"https://www.ams.org/tran/1985-287-02/S0002-9947-1985-0768729-X/S0002-9947-1985-0768729-X.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/tran/1985-287-02/S0002-9947-1985-0768729-X/S0002-9947-1985-0768729-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032063874","display_name":"C. Bruce Hughes","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"C. Bruce Hughes","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5032063874"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2724,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.76623015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"287","issue":"2","first_page":"621","last_page":"621"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.6786999702453613,"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":0.6786999702453613,"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":0.31299999356269836,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.0017000000225380063,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hilbert-cube-manifolds","display_name":"Hilbert cube manifolds","score":0.9850000143051147},{"id":"https://openalex.org/keywords/homotopy-equivalence","display_name":"homotopy equivalence","score":0.8579999804496765},{"id":"https://openalex.org/keywords/approximate-fibrations","display_name":"approximate fibrations","score":0.8389999866485596},{"id":"https://openalex.org/keywords/homotopy-groups","display_name":"homotopy groups","score":0.8799999952316284},{"id":"https://openalex.org/keywords/algebraic-k-theory","display_name":"algebraic K-theory","score":0.8659999966621399}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8551827669143677},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.7551900148391724},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6387617588043213},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.556433916091919},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5513588190078735},{"id":"https://openalex.org/C147688034","wikidata":"https://www.wikidata.org/wiki/Q1626416","display_name":"Homotopy group","level":3,"score":0.508611798286438},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4608032703399658},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.4314389228820801},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42669880390167236},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2732824385166168},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21486368775367737}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0002-9947-1985-0768729-x","doi":"https://doi.org/10.1090/s0002-9947-1985-0768729-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1985-0768729-x","pdf_url":"https://www.ams.org/tran/1985-287-02/S0002-9947-1985-0768729-X/S0002-9947-1985-0768729-X.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},{"id":"doi:10.2307/1999665","doi":"https://doi.org/10.2307/1999665","is_oa":false,"landing_page_url":"https://doi.org/10.2307/1999665","pdf_url":null,"source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.433.6454","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.433.6454","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.vanderbilt.edu/~hughescb/Publications/1985_Bounded_homotopy_equivalences_of_Hilbert_cube_manifolds.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0002-9947-1985-0768729-x","doi":"https://doi.org/10.1090/s0002-9947-1985-0768729-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9947-1985-0768729-x","pdf_url":"https://www.ams.org/tran/1985-287-02/S0002-9947-1985-0768729-X/S0002-9947-1985-0768729-X.pdf","source":{"id":"https://openalex.org/S60030702","display_name":"Transactions of the American Mathematical Society","issn_l":"0002-9947","issn":["0002-9947","1088-6850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1993673539.pdf","grobid_xml":"https://content.openalex.org/works/W1993673539.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W582494080","https://openalex.org/W1525008043","https://openalex.org/W1585906134","https://openalex.org/W1964949286","https://openalex.org/W1967031702","https://openalex.org/W1972847067","https://openalex.org/W1979546492","https://openalex.org/W1990918532","https://openalex.org/W1998640212","https://openalex.org/W2000549181","https://openalex.org/W2005235405","https://openalex.org/W2017002113","https://openalex.org/W2017655138","https://openalex.org/W2019918360","https://openalex.org/W2025319471","https://openalex.org/W2042551162","https://openalex.org/W2044781317","https://openalex.org/W2047896077","https://openalex.org/W2064999865","https://openalex.org/W2069265968","https://openalex.org/W2070594927","https://openalex.org/W2078172218","https://openalex.org/W2082525471","https://openalex.org/W2122778257","https://openalex.org/W2143677236","https://openalex.org/W2150377316","https://openalex.org/W2325170555","https://openalex.org/W2601697325","https://openalex.org/W3043060850","https://openalex.org/W4211208245","https://openalex.org/W4213152686","https://openalex.org/W4244578284","https://openalex.org/W6602379068","https://openalex.org/W6607175793","https://openalex.org/W6834620246"],"related_works":["https://openalex.org/W2019455149","https://openalex.org/W1970118475","https://openalex.org/W172366429","https://openalex.org/W2018998924","https://openalex.org/W2056966080","https://openalex.org/W117536794","https://openalex.org/W1980800551","https://openalex.org/W2042551162","https://openalex.org/W2952239574","https://openalex.org/W2053242197"],"abstract_inverted_index":{"Let":[0],"$M$":[1],"and":[2],"$F$":[3,9],"be":[4],"Hilbert":[5],"cube":[6],"manifolds":[7],"with":[8],"compact.":[10],"The":[11],"purpose":[12],"of":[13,70,82,93],"this":[14],"paper":[15],"is":[16,64],"to":[17,66],"study":[18],"homotopy":[19,37,80],"equivalences":[20,38],"$f:M":[21],"\\to":[22],"{{\\mathbf":[23],"{R}}^m}":[24,46,61,75,86],"\\times":[25,47,62,76,87],"F$":[26],"which":[27],"have":[28],"bounded":[29,71],"control":[30],"in":[31,91],"the":[32,49,67,79,94],"${{\\mathbf":[33,74],"{R}}^m}$-direction.":[34],"Roughly,":[35],"these":[36],"form":[39],"a":[40],"semi-simplicial":[41,68],"complex":[42,69],"$\\mathcal":[43,58,83],"{W}\\mathcal":[44,59,84],"{H}({{\\mathbf":[45,60,85],"F)$,":[48],"controlled":[50],"Whitehead":[51],"space.":[52],"Using":[53],"results":[54],"about":[55],"approximate":[56],"fibrations,":[57],"F)$":[63,88],"related":[65],"concordances":[72],"on":[73],"F$.":[77],"Then":[78],"groups":[81],"are":[89],"computed":[90],"terms":[92],"lower":[95],"algebraic":[96],"$K$-theoretic":[97],"functors":[98],"${K_{":[99],"-":[100],"i}}$.":[101]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
