{"id":"https://openalex.org/W1711774989","doi":"https://doi.org/10.1142/s0218196703001389","title":"Hurwitz Equivalence in the Braid Group B<sub>3</sub>","display_name":"Hurwitz Equivalence in the Braid Group B<sub>3</sub>","publication_year":2003,"publication_date":"2003-06-01","ids":{"openalex":"https://openalex.org/W1711774989","doi":"https://doi.org/10.1142/s0218196703001389","mag":"1711774989"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196703001389","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196703001389","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/A5083715192","display_name":"T. Ben-Itzhak","orcid":null},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"T. Ben-Itzhak","raw_affiliation_strings":["Department of Mathematics, Bar-Ilan University,  52900 Ramat Gan, Israel","Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bar-Ilan University,  52900 Ramat Gan, Israel","institution_ids":["https://openalex.org/I13955877"]},{"raw_affiliation_string":"Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel,","institution_ids":["https://openalex.org/I13955877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091766722","display_name":"Mina Teicher","orcid":"https://orcid.org/0000-0003-1700-9709"},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"M. Teicher","raw_affiliation_strings":["Department of Mathematics, Bar-Ilan University,  52900 Ramat Gan, Israel","Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bar-Ilan University,  52900 Ramat Gan, Israel","institution_ids":["https://openalex.org/I13955877"]},{"raw_affiliation_string":"Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel,","institution_ids":["https://openalex.org/I13955877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083715192"],"corresponding_institution_ids":["https://openalex.org/I13955877"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07579157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"03","first_page":"277","last_page":"286"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9950000047683716,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9950000047683716,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9904000163078308,"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/mathematics","display_name":"Mathematics","score":0.864916205406189},{"id":"https://openalex.org/keywords/diffeomorphism","display_name":"Diffeomorphism","score":0.6592661142349243},{"id":"https://openalex.org/keywords/braid-group","display_name":"Braid group","score":0.6323555707931519},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6038928031921387},{"id":"https://openalex.org/keywords/braid","display_name":"Braid","score":0.5973191261291504},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5898185968399048},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5427056550979614},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.48405805230140686},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4753665328025818},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4546603858470917},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15835031867027283},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05354204773902893}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.864916205406189},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.6592661142349243},{"id":"https://openalex.org/C33840335","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid group","level":2,"score":0.6323555707931519},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6038928031921387},{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.5973191261291504},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5898185968399048},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5427056550979614},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.48405805230140686},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4753665328025818},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4546603858470917},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15835031867027283},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05354204773902893},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196703001389","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196703001389","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.1368","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.1368","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0101233v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W966425145","https://openalex.org/W2152651756","https://openalex.org/W2617213545","https://openalex.org/W4236482227"],"related_works":["https://openalex.org/W2945083448","https://openalex.org/W4245342330","https://openalex.org/W2094080661","https://openalex.org/W1859278099","https://openalex.org/W2951598886","https://openalex.org/W4363678311","https://openalex.org/W4298849474","https://openalex.org/W4301028463","https://openalex.org/W2503435930","https://openalex.org/W1846674139"],"abstract_inverted_index":{"In":[0,13],"this":[1,152],"paper":[2,153],"we":[3,15],"prove":[4,16],"certain":[5],"Hurwitz":[6,73,132],"equivalence":[7,133],"properties":[8],"of":[9,26,30,96,120,134,145,151],"B":[10],"n":[11,19],".":[12],"particular":[14],"that":[17,106,110],"for":[18],"=":[20],"3":[21],"every":[22],"two":[23],"Artin":[24],"factorizations":[25],"[Formula:":[27],"see":[28],"text]":[29],"the":[31,94,159],"form":[32],"H":[33,37,61],"i":[34,38,49],"1":[35,43,59,65],"\u22ef":[36,44],"6":[39,47],",":[40,51,60,66],"F":[41,45,67],"j":[42,46,52],"(with":[48],"k":[50,53],"\u2208":[54],"{1,":[55],"2})":[56],"where":[57],"{H":[58],"2":[62,68],"},":[63],"{F":[64],"}":[69],"are":[70,72,111,117,142],"frames,":[71],"equivalent.":[74],"The":[75,88,148],"proof":[76],"provided":[77],"here":[78],"is":[79,103],"geometric,":[80],"based":[81,130],"on":[82,131],"a":[83,127],"newly":[84],"defined":[85],"frame":[86],"type.":[87],"results":[89],"will":[90,154],"be":[91],"applied":[92],"to":[93,100,113,136,157],"classification":[95],"algebraic":[97],"surfaces":[98,109,140],"up":[99],"deformation.":[101],"It":[102],"already":[104],"known":[105],"there":[107],"exist":[108],"diffeomorphic":[112,139],"each":[114,121,146],"other":[115,122],"but":[116],"not":[118,143],"deformations":[119],"(Manetti's":[123],"example).":[124],"We":[125],"construct":[126],"new":[128,160],"invariant":[129],"factorizations,":[135],"distinguish":[137],"among":[138],"which":[141],"deformation":[144],"other.":[147],"main":[149],"result":[150],"help":[155],"us":[156],"compute":[158],"invariant.":[161]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
