{"id":"https://openalex.org/W2040460101","doi":"https://doi.org/10.1142/s0218196703001456","title":"Logical Distinction Between Diagrammatic and Cohen\u2013Lyndon Asphericity","display_name":"Logical Distinction Between Diagrammatic and Cohen\u2013Lyndon Asphericity","publication_year":2003,"publication_date":"2003-06-01","ids":{"openalex":"https://openalex.org/W2040460101","doi":"https://doi.org/10.1142/s0218196703001456","mag":"2040460101"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196703001456","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196703001456","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5053064784","display_name":"Igor Marko Biskup","orcid":null},"institutions":[{"id":"https://openalex.org/I131221577","display_name":"Bucknell University","ror":"https://ror.org/00fc1qt65","country_code":"US","type":"education","lineage":["https://openalex.org/I131221577"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Igor Biskup","raw_affiliation_strings":["Department of Mathematics, 380 Olin Science Building, Bucknell University, Lewisburg, PA 17837, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, 380 Olin Science Building, Bucknell University, Lewisburg, PA 17837, USA","institution_ids":["https://openalex.org/I131221577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5053064784"],"corresponding_institution_ids":["https://openalex.org/I131221577"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1437542,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"03","first_page":"241","last_page":"253"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9968000054359436,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/argument","display_name":"Argument (complex analysis)","score":0.7788450121879578},{"id":"https://openalex.org/keywords/presentation","display_name":"Presentation (obstetrics)","score":0.761139988899231},{"id":"https://openalex.org/keywords/diagrammatic-reasoning","display_name":"Diagrammatic reasoning","score":0.7393152713775635},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6998410820960999},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6111687421798706},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4803544282913208},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.44846707582473755},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4426734447479248},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37858426570892334},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.2114560902118683},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21086403727531433},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.1928042769432068},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16606661677360535},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.13881263136863708},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09503304958343506},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.07196339964866638}],"concepts":[{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.7788450121879578},{"id":"https://openalex.org/C2777601897","wikidata":"https://www.wikidata.org/wiki/Q3409113","display_name":"Presentation (obstetrics)","level":2,"score":0.761139988899231},{"id":"https://openalex.org/C106624574","wikidata":"https://www.wikidata.org/wiki/Q5270387","display_name":"Diagrammatic reasoning","level":2,"score":0.7393152713775635},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6998410820960999},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6111687421798706},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4803544282913208},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.44846707582473755},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4426734447479248},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37858426570892334},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.2114560902118683},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21086403727531433},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.1928042769432068},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16606661677360535},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.13881263136863708},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09503304958343506},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07196339964866638},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196703001456","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196703001456","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1963609671","https://openalex.org/W1994550804","https://openalex.org/W1994885090","https://openalex.org/W2016632263","https://openalex.org/W2021164857","https://openalex.org/W2028713172","https://openalex.org/W2044205806","https://openalex.org/W2087707125","https://openalex.org/W2990802139","https://openalex.org/W3193997241","https://openalex.org/W3194331646","https://openalex.org/W4250077446","https://openalex.org/W4292101339"],"related_works":["https://openalex.org/W3003518673","https://openalex.org/W2243494072","https://openalex.org/W2933723564","https://openalex.org/W4288417689","https://openalex.org/W1582653816","https://openalex.org/W3036486735","https://openalex.org/W2137260079","https://openalex.org/W2134137410","https://openalex.org/W1785591160","https://openalex.org/W1557478423"],"abstract_inverted_index":{"We":[0,179],"resolve":[1],"the":[2,5,11,16,20,56,77,95,132,169,186,198,219,228,237],"status":[3,167],"of":[4,19,73,79,94,105,118,121,131,139,168,214,239,245],"implication":[6,171,187],"CLA":[7,188],"\u21d2":[8,189],"DA":[9,35,190],"in":[10,47,124],"negative":[12],"by":[13],"showing":[14],"that":[15,43,86,116,148,193,218,227],"two-dimensional":[17,65,97,151],"model":[18],"group":[21,84],"presentation":[22,199,220,229],"(a,":[23,200],"b":[24,27,31,201,204],":":[25,202],"a,":[26,203],"-1":[28,30,32,207],"aba":[29,206],")":[33,208],"is":[34,60,155,161,221,236],"but":[36],"not":[37,90],"CLA.":[38,232],"This":[39,68],"settles":[40],"a":[41,61,128,150,250],"question":[42,57,69],"has":[44],"been":[45,173],"addressed":[46],"[2,":[48],"7,":[49],"10,":[50],"11].":[51],"In":[52,111],"1941,":[53],"Whitehead":[54],"posed":[55],"whether":[58],"asphericity":[59,93,106,122],"hereditary":[62],"property":[63],"for":[64,83,92,185],"CW":[66,152],"complexes.":[67],"remains":[70],"unanswered.":[71],"Out":[72],"its":[74],"study":[75],"developed":[76],"formulation":[78],"several":[80],"combinatorial":[81],"properties":[82],"presentations":[85],"are":[87,107,123,135],"sufficient":[88],"(but":[89],"necessary)":[91],"associated":[96],"model.":[98],"The":[99,166],"logical":[100],"relationships":[101],"between":[102],"these":[103,119],"flavors":[104,120,134],"just":[108],"partially":[109],"understood.":[110],"this":[112,177],"article":[113],"we":[114,247],"show":[115],"two":[117],"fact":[125],"distinct.":[126,136],"As":[127],"consequence,":[129],"all":[130],"known":[133],"An":[137],"argument":[138,225],"Lyndon":[140],"and":[141,191,242],"Schupp":[142],"[5,":[143],"III":[144],"Property":[145],"10.6]":[146],"shows":[147,226],"if":[149],"complex":[153],"K":[154,160],"Cohen\u2013Lyndon":[156],"aspherical":[157,164],"(CLA),":[158],"then":[159],"also":[162],"diagrammatically":[163],"(DA).":[165],"reverse":[170],"had":[172],"open":[174],"prior":[175],"to":[176],"writing.":[178],"will":[180,248],"present":[181],"an":[182],"alternative":[183],"proof":[184],"demonstrate":[192],"every":[194],"spherical":[195,240],"picture":[196,243],"over":[197],"-2":[205],"can":[209],"be":[210,231],"reduced":[211],"without":[212],"insertions":[213],"dipoles,":[215],"thus":[216],"concluding":[217],"DA.":[222],"A":[223],"straightforward":[224],"cannot":[230],"Our":[233],"main":[234],"tool":[235],"theory":[238],"pictures":[241],"moves":[244],"which":[246],"give":[249],"short":[251],"survey.":[252]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}