{"id":"https://openalex.org/W3046356475","doi":null,"title":"Combinatorics of Milnor fibres of reflection arrangements","display_name":"Combinatorics of Milnor fibres of reflection arrangements","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3046356475","mag":"3046356475"},"language":"en","primary_location":{"id":"pmh:oai:ses.library.usyd.edu.au:2123/22985","doi":null,"is_oa":false,"landing_page_url":"https://hdl.handle.net/2123/22985","pdf_url":null,"source":{"id":"https://openalex.org/S4306402414","display_name":"The Sydney eScholarship Repository (The University of Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I129604602","host_organization_name":"The University of Sydney","host_organization_lineage":["https://openalex.org/I129604602"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"},"parent_works":[],"lineage":["https://openalex.org/W3046356475"],"child_works_count":0,"type":"dissertation","is_traditional":true,"indexed_in":[],"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/A5100354779","display_name":"Yang Zhang","orcid":"https://orcid.org/0000-0003-2085-337X","observed_orcids":["https://orcid.org/0000-0003-2085-337X","https://orcid.org/0000-0002-7709-7037"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yang Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5100354779"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9692000150680542,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9692000150680542,"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"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.013299999758601189,"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":0.010200000368058681,"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/milnor-fiber","display_name":"Milnor fiber","score":0.9350000023841858},{"id":"https://openalex.org/keywords/reflection-arrangements","display_name":"reflection arrangements","score":0.9760000109672546},{"id":"https://openalex.org/keywords/finite-coxeter-groups","display_name":"finite Coxeter groups","score":0.9810000061988831},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"simplicial complexes","score":0.8330000042915344},{"id":"https://openalex.org/keywords/integral-homology","display_name":"integral homology","score":0.9660000205039978},{"id":"https://openalex.org/keywords/chain-complexes","display_name":"chain complexes","score":0.8119999766349792},{"id":"https://openalex.org/keywords/orlik-solomon-algebra","display_name":"Orlik-Solomon algebra","score":0.8610000014305115},{"id":"https://openalex.org/keywords/monodromy","display_name":"monodromy","score":0.7400000095367432},{"id":"https://openalex.org/keywords/discriminant","display_name":"discriminant","score":0.7210000157356262}],"concepts":[{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.5282456278800964},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39054644107818604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3714487552642822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25622832775115967},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10024461150169373}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:ses.library.usyd.edu.au:2123/22985","doi":null,"is_oa":false,"landing_page_url":"https://hdl.handle.net/2123/22985","pdf_url":null,"source":{"id":"https://openalex.org/S4306402414","display_name":"The Sydney eScholarship Repository (The University of Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I129604602","host_organization_name":"The University of Sydney","host_organization_lineage":["https://openalex.org/I129604602"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Thesis"},{"id":"mag:3046356475","doi":null,"is_oa":false,"landing_page_url":"https://ses.library.usyd.edu.au/handle/2123/22985","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4319066585","https://openalex.org/W4396941657","https://openalex.org/W2758455286","https://openalex.org/W2027414854","https://openalex.org/W7221399908","https://openalex.org/W2053881820","https://openalex.org/W7100513982","https://openalex.org/W4253835344","https://openalex.org/W1638176826","https://openalex.org/W2058413984"],"abstract_inverted_index":{"Recently,":[0],"Brady,":[1,257],"Falk":[2,258],"and":[3,119,128,145,211,259],"Watt":[4],"introduced":[5],"a":[6,25,36,56,78,94,154],"simplicial":[7,50],"complex":[8,58,204],"which":[9,121,157],"has":[10,158],"the":[11,15,20,41,82,88,98,107,125,130,133,148,162,178,184,191,199,212,228,231,240,244,248,254],"homotopy":[12],"type":[13],"of":[14,19,45,59,70,81,93,97,103,110,132,143,169,177,183,190,201,208,230,233,242,247,250,256],"Milnor":[16,245],"fibre":[17,246],"F_Q":[18,46],"reflection":[21],"arrangement":[22],"associated":[23],"to":[24,34,39,68,77,106,124,159,197,239],"finite":[26],"Coxeter":[27],"group":[28,74,84,92,182],"W.":[29,104,251],"This":[30,194,252],"thesis":[31],"is":[32,55,66,75,139,151,237],"devoted":[33],"developing":[35],"combinatorial":[37,155],"approach":[38],"computing":[40],"integral":[42,64,83],"homology":[43,65,91,131,181,200,229,241],"groups":[44,62,236],"based":[47],"on":[48],"this":[49],"complex.":[51,222],"Our":[52],"main":[53],"result":[54,255],"chain":[57,73,203,221,235],"free":[60],"abelian":[61],"whose":[63],"isomorphic":[67,76,115,238],"that":[69,227],"F_Q.":[71],"Each":[72],"tensor":[79],"product":[80],"ring":[85],"ZW":[86],"with":[87,161],"top":[89,179],"reduced":[90,180],"rank-selected":[95,188],"subposet":[96,189],"noncrossing":[99],"partition":[100],"(NCP)":[101],"lattice":[102,109],"Associated":[105],"NCP":[108,134,192],"W":[111,210],"we":[112,225],"define":[113],"two":[114],"graded":[116],"Z-algebras":[117],"A":[118,138],"B,":[120],"have":[122],"similarities":[123],"Orlik-Solomon":[126],"algebra":[127,137,149],"characterise":[129],"lattice.":[135,193],"The":[136,206],"defined":[140,152],"in":[141,153],"terms":[142],"generators":[144],"relations,":[146],"while":[147],"B":[150,170],"manner":[156],"do":[160],"Hurwitz":[163],"actions.":[164],"In":[165,223],"particular,":[166,224],"each":[167],"element":[168],"(or":[171],"A)":[172],"produces":[173],"an":[174],"explicit":[175],"cycle":[176],"corresponding":[185],"interval":[186],"or":[187],"permits":[195],"us":[196],"calculate":[198],"our":[202,220],"computationally.":[205],"actions":[207],"both":[209],"monodromy":[213],"may":[214],"also":[215],"be":[216],"partly":[217],"described":[218],"by":[219],"prove":[226],"subcomplex":[232],"W-invariant":[234],"F_P=F_Q/W,":[243],"discriminant":[249],"recovers":[253],"Watt.":[260]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2020-08-07T00:00:00"}