{"id":"https://openalex.org/W2087864003","doi":"https://doi.org/10.1155/2007/87404","title":"<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>T</mml:mi></mml:math>-Homotopy and Refinement of Observation\u2014Part II: Adding New<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>T</mml:mi></mml:math>-Homotopy Equivalences","display_name":"<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>T</mml:mi></mml:math>-Homotopy and Refinement of Observation\u2014Part II: Adding New<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>T</mml:mi></mml:math>-Homotopy Equivalences","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2087864003","doi":"https://doi.org/10.1155/2007/87404","mag":"2087864003"},"language":"en","primary_location":{"id":"doi:10.1155/2007/87404","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/87404","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2007/087404.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2007/087404.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076299516","display_name":"Philippe Gaucher","orcid":"https://orcid.org/0000-0003-0287-6252"},"institutions":[{"id":"https://openalex.org/I4210139011","display_name":"Laboratory Preuves, Programmes et Syst\u00e8mes","ror":"https://ror.org/046p9e825","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I4210139011","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Philippe Gaucher","raw_affiliation_strings":["PPS - Preuves, Programmes et Syst\u00e8mes (Universit\u00e9 Paris Diderot, B\u00e2t. Sophie Germain, case postale 7014, 75205 Paris Cedex 13 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PPS - Preuves, Programmes et Syst\u00e8mes (Universit\u00e9 Paris Diderot, B\u00e2t. Sophie Germain, case postale 7014, 75205 Paris Cedex 13 - France)","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210139011"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076299516"],"corresponding_institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210139011"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.3075,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.7817285,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2007","issue":null,"first_page":"1","last_page":"20"},"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":0.9987000226974487,"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":0.9987000226974487,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.989300012588501,"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":0.9545000195503235,"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/algorithm","display_name":"Algorithm","score":0.6123438477516174},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5150880217552185},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.48550939559936523},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.47791701555252075},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3568040132522583},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3536633849143982},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30860865116119385},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.20789563655853271},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16176173090934753}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6123438477516174},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5150880217552185},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.48550939559936523},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.47791701555252075},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3568040132522583},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3536633849143982},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30860865116119385},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.20789563655853271},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16176173090934753}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2007/87404","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/87404","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2007/087404.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0505328","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0505328","pdf_url":"https://arxiv.org/pdf/math/0505328","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-00150917v1","is_oa":false,"landing_page_url":"https://hal.science/hal-00150917","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, 2007, 2007, Article ID 87404, 20 p. &#x27E8;10.1155/2007/87404&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:d22ff61cb72541ef82972bd1c013a1ae","is_oa":true,"landing_page_url":"https://doaj.org/article/d22ff61cb72541ef82972bd1c013a1ae","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2007 (2007)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2007/87404","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/87404","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2007/087404.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2087864003.pdf","grobid_xml":"https://content.openalex.org/works/W2087864003.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W78673101","https://openalex.org/W94242635","https://openalex.org/W591754403","https://openalex.org/W1481441183","https://openalex.org/W1526004405","https://openalex.org/W1583122470","https://openalex.org/W1792107284","https://openalex.org/W2001420945","https://openalex.org/W2012099811","https://openalex.org/W2014838036","https://openalex.org/W2102075603","https://openalex.org/W2103602777","https://openalex.org/W2112236959","https://openalex.org/W2117377773","https://openalex.org/W2121162230","https://openalex.org/W2129539457","https://openalex.org/W2136289172","https://openalex.org/W2142748370","https://openalex.org/W2274725143","https://openalex.org/W2949145592","https://openalex.org/W2950523604"],"related_works":["https://openalex.org/W2961085424","https://openalex.org/W4306674287","https://openalex.org/W3046775127","https://openalex.org/W3107602296","https://openalex.org/W3170094116","https://openalex.org/W4386462264","https://openalex.org/W4364306694","https://openalex.org/W4312192474","https://openalex.org/W4283697347","https://openalex.org/W4210805261"],"abstract_inverted_index":{"This":[0,42],"paper":[1],"is":[2,20,55,66,77,93,102],"the":[3,23,32,35,39,58,86,107],"second":[4],"part":[5],"of":[6,9,17,34,46,60,62,85,91,110],"a":[7,12,44,78],"series":[8],"papers":[10,109],"about":[11],"new":[13,50],"notion":[14],"of<mml:math":[15,26,52],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>T</mml:mi></mml:math>-homotopy":[16,27,53,75,80],"flows.":[18],"It":[19],"proved":[21,67],"that":[22,68],"old":[24],"definition":[25,51],"equivalence":[28,54,76],"does":[29],"not":[30],"allow":[31],"identification":[33],"directed":[36],"segment":[37],"with":[38],"3-dimensional":[40],"cube.":[41],"contradicts":[43],"paradigm":[45],"dihomotopy":[47],"theory.":[48],"A":[49],"proposed,":[56],"following":[57],"intuition":[59],"refinement":[61],"observation.":[63],"And":[64],"it":[65],"up":[69],"to":[70],"weak<mml:math":[71,87],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>S</mml:mi></mml:math>-homotopy,":[72],"an":[73],"old<mml:math":[74],"new<mml:math":[79],"equivalence.":[81],"The":[82,99],"left":[83],"properness":[84],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>S</mml:mi></mml:math>-homotopy":[88],"model":[89],"category":[90],"flows":[92],"also":[94],"established":[95],"in":[96,106],"this":[97,111],"part.":[98],"latter":[100],"fact":[101],"used":[103],"several":[104],"times":[105],"next":[108],"series.":[112]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2016-06-24T00:00:00"}
