{"id":"https://openalex.org/W7207638156","doi":"https://doi.org/10.48550/arxiv.2609.02123","title":"Groups of Transverse Stratifications and the Hierarchy of Configuration Spaces","display_name":"Groups of Transverse Stratifications and the Hierarchy of Configuration Spaces","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7207638156","doi":"https://doi.org/10.48550/arxiv.2609.02123"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.02123","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02123","pdf_url":"https://arxiv.org/pdf/2609.02123","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.02123","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112766029","display_name":"Vassily Olegovich Manturov","orcid":"https://orcid.org/0000-0003-3061-7151","observed_orcids":["https://orcid.org/0000-0003-3061-7151"]},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Manturov, Vassily Olegovich","raw_affiliation_strings":["Moscow Institute of Physics and Technology (MIPT)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow Institute of Physics and Technology (MIPT)","institution_ids":["https://openalex.org/I153845743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112766029"],"corresponding_institution_ids":["https://openalex.org/I153845743"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9854000210762024,"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":0.9854000210762024,"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":0.011599999852478504,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0012000000569969416,"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/moduli-spaces","display_name":"moduli spaces","score":0.8029999732971191},{"id":"https://openalex.org/keywords/fundamental-group","display_name":"fundamental group","score":0.5429999828338623},{"id":"https://openalex.org/keywords/configuration-space","display_name":"configuration space","score":0.7670000195503235},{"id":"https://openalex.org/keywords/algebraic-curves","display_name":"algebraic curves","score":0.8420000076293945},{"id":"https://openalex.org/keywords/transversality","display_name":"transversality","score":0.8159999847412109}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7778000235557556},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.6983000040054321},{"id":"https://openalex.org/C24167531","wikidata":"https://www.wikidata.org/wiki/Q2300767","display_name":"Transversality","level":2,"score":0.5860999822616577},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.5763000249862671},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.53329998254776},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4431999921798706},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.4251999855041504},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.4219000041484833},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.40549999475479126},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38580000400543213},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3750999867916107},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.37389999628067017},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C3387666","wikidata":"https://www.wikidata.org/wiki/Q6889798","display_name":"Moduli of algebraic curves","level":3,"score":0.3328999876976013},{"id":"https://openalex.org/C192943249","wikidata":"https://www.wikidata.org/wiki/Q1893382","display_name":"Stratification (seeds)","level":5,"score":0.32359999418258667},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29910001158714294},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C2777283802","wikidata":"https://www.wikidata.org/wiki/Q2042963","display_name":"Picard group","level":3,"score":0.25540000200271606},{"id":"https://openalex.org/C2780130068","wikidata":"https://www.wikidata.org/wiki/Q2208651","display_name":"Transversal (combinatorics)","level":2,"score":0.25380000472068787},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.02123","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02123","pdf_url":"https://arxiv.org/pdf/2609.02123","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.02123","doi":"https://doi.org/10.48550/arxiv.2609.02123","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.02123","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.02123","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02123","pdf_url":"https://arxiv.org/pdf/2609.02123","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207638156.pdf","grobid_xml":"https://content.openalex.org/works/W7207638156.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2963060824","https://openalex.org/W3129438977","https://openalex.org/W7202211131"],"related_works":["https://openalex.org/W1686380072","https://openalex.org/W1998458603","https://openalex.org/W7098712531","https://openalex.org/W4250361518","https://openalex.org/W7098393198","https://openalex.org/W2308444046","https://openalex.org/W2323738001","https://openalex.org/W2970233734","https://openalex.org/W2418232708","https://openalex.org/W7099907549"],"abstract_inverted_index":{"We":[0,84],"introduce":[1],"a":[2,16,22,30,57],"broad":[3],"family":[4],"of":[5,12,19,36,60,66,101,104],"groups":[6],"$G(\u0393)$":[7],"associated":[8],"with":[9],"transverse":[10,79],"stratifications":[11,20,90],"moduli":[13,38,87],"spaces.":[14],"For":[15],"wide":[17],"class":[18],"satisfying":[21],"natural":[23],"local":[24],"condition":[25],"(transverse":[26],"niceness),":[27],"we":[28,97],"construct":[29],"homomorphism":[31],"from":[32],"the":[33,37,41,52,61,67,78,99,107,115,128],"fundamental":[34],"group":[35,43],"space":[39],"to":[40,71],"corresponding":[42],"$G(\u0393)$.":[44],"This":[45],"general":[46,122],"theorem,":[47],"which":[48],"is":[49,70,125],"proved":[50],"in":[51,106,127],"companion":[53],"paper":[54,69],"\\cite{Manturov2026},":[55],"provides":[56],"far-reaching":[58],"generalization":[59],"$G_n^k$-theory.":[62],"The":[63,121],"main":[64],"goal":[65],"present":[68],"discuss":[72],"numerous":[73],"examples":[74],"and":[75,89,113],"situations":[76],"where":[77],"niceness":[80],"property":[81,117],"actually":[82],"occurs.":[83],"describe":[85],"various":[86],"spaces":[88,103],"that":[91],"are":[92],"transversely":[93],"nice.":[94],"In":[95],"particular,":[96],"study":[98],"hierarchy":[100,123],"configuration":[102],"points":[105],"plane":[108],"defined":[109],"by":[110],"algebraic":[111],"curves":[112],"establish":[114],"transversality":[116],"for":[118],"conic":[119],"configurations.":[120],"problem":[124],"formulated":[126],"final":[129],"section.":[130]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-04T00:00:00"}