{"id":"https://openalex.org/W7225170486","doi":"https://doi.org/10.5281/zenodo.23918254","title":"Asphericity and Stable Complexity of Graph Configuration Spaces with Sinks","display_name":"Asphericity and Stable Complexity of Graph Configuration Spaces with Sinks","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7225170486","doi":"https://doi.org/10.5281/zenodo.23918254"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23918254","doi":"https://doi.org/10.5281/zenodo.23918254","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23918254","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23918254","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120295250","display_name":"\u041c\u0430\u043a\u0441\u0438\u043c \u0427\u0443\u0440\u0438\u043b\u043e\u0432","orcid":"https://orcid.org/0009-0009-1690-2934","observed_orcids":["https://orcid.org/0009-0009-1690-2934"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Churilov, Maxim","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0009-1690-2934","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5120295250"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.8125,"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":0.8125,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.17820000648498535,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.0012000000569969416,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/configuration-space","display_name":"configuration space","score":0.5709999799728394},{"id":"https://openalex.org/keywords/asphericity","display_name":"asphericity","score":0.9089999794960022},{"id":"https://openalex.org/keywords/topological-complexity","display_name":"topological complexity","score":0.7739999890327454},{"id":"https://openalex.org/keywords/deformation-retraction","display_name":"deformation retraction","score":0.7310000061988831},{"id":"https://openalex.org/keywords/higher-homotopy-groups","display_name":"higher homotopy groups","score":0.8489999771118164},{"id":"https://openalex.org/keywords/finite-covers","display_name":"finite covers","score":0.4259999990463257},{"id":"https://openalex.org/keywords/path-components","display_name":"path components","score":0.4020000100135803}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8389000296592712},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.6381999850273132},{"id":"https://openalex.org/C143782950","wikidata":"https://www.wikidata.org/wiki/Q40460","display_name":"Orbifold","level":2,"score":0.5548999905586243},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5192999839782715},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4887999892234802},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.4309999942779541},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4284999966621399},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34290000796318054},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.33980000019073486},{"id":"https://openalex.org/C90738871","wikidata":"https://www.wikidata.org/wiki/Q41642869","display_name":"Configuration space","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.31700000166893005},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29660001397132874},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28940001130104065},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.2888000011444092},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C169611556","wikidata":"https://www.wikidata.org/wiki/Q230689","display_name":"Contractible space","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.26170000433921814},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C191752858","wikidata":"https://www.wikidata.org/wiki/Q6358325","display_name":"n-connected","level":3,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23918254","doi":"https://doi.org/10.5281/zenodo.23918254","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23918254","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23918255","doi":"https://doi.org/10.5281/zenodo.23918255","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23918255","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23918254","doi":"https://doi.org/10.5281/zenodo.23918254","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23918254","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4402270496","https://openalex.org/W2606796000","https://openalex.org/W2776980374","https://openalex.org/W4400601285","https://openalex.org/W2739391825","https://openalex.org/W2888529337","https://openalex.org/W3034660692","https://openalex.org/W2806091151","https://openalex.org/W4312897525","https://openalex.org/W4320342421"],"abstract_inverted_index":{"Let":[0],"\\(G\\)":[1],"be":[2,10],"a":[3,11,60,64,165],"finite":[4,138],"graph":[5],"and":[6,105,119],"let":[7],"\\(S\\subseteq":[8],"V(G)\\)":[9],"set":[12],"of":[13,26,93,101,159],"vertices":[14],"at":[15,135],"which":[16],"collisions":[17],"are":[18],"permitted.":[19],"We":[20],"prove":[21],"that":[22],"every":[23,120],"path":[24],"component":[25],"the":[27,37,42,50,91,94,98,131,144,155,160],"ordered":[28],"sink":[29],"configuration":[30],"space":[31,72],"\\(\\Conf_n(G,S)\\)":[32],"is":[33,73,90,128,148],"aspherical":[34,74],"by":[35,154],"applying":[36],"cubical":[38],"link":[39],"criterion":[40],"to":[41,142,150],"Chettih--L\u00fctgehetmann":[43],"model.":[44],"The":[45,123],"unordered":[46,71],"analogue":[47],"fails.":[48],"For":[49],"\\(m\\)-petal":[51],"rose":[52],"\\(R_m\\)":[53],"with":[54],"its":[55,84],"unique":[56],"vertex":[57],"\\(v\\)":[58],"declared":[59],"sink,":[61],"we":[62],"construct":[63],"deformation":[65],"retraction":[66],"\\(\\BConf_n(R_m,\\{v\\})\\simeq":[67],"\\sk_{\\min\\{n,m\\}}(\\T^m)\\).":[68],"Consequently":[69],"this":[70],"exactly":[75],"for":[76,114],"\\(n\\leq1\\)":[77],"or":[78],"\\(n\\geq":[79],"m\\).":[80],"If":[81],"\\(2\\leq":[82],"d=\\min\\{n,m\\}<m\\),":[83],"first":[85],"nonzero":[86],"higher":[87],"homotopy":[88,132],"group":[89],"image":[92],"\\((d+1)\\)-st":[95],"differential":[96],"in":[97],"Laurent--Koszul":[99],"resolution":[100],"\\(\\Z\\)":[102],"over":[103],"\\(\\Z[\\Z^m]\\),":[104],"has":[106],"module":[107],"rank":[108],"\\(\\binom{m-1}{d}\\).":[109],"In":[110],"particular,":[111],"\\(\\pi_2(\\BConf_2(R_3,\\{v\\}))\\cong\\Z[\\Z^3]\\).":[112],"Finally,":[113],"reduced":[115],"sequential":[116],"topological":[117],"complexity":[118],"\\(r\\geq2\\),":[121],"\\(\\TC_r\\bigl(\\BConf_n(R_m,\\{v\\})\\bigr)=\\min\\{r\\min(n,m),(r-1)m\\}\\).":[122],"sharp":[124,166],"numerical":[125],"stabilization":[126],"threshold":[127],"\\(\\lceil(r-1)m/r\\rceil\\),":[129],"while":[130],"type":[133],"stabilizes":[134],"\\(n=m\\).":[136],"Any":[137],"torsion-free":[139],"cover":[140],"used":[141],"remove":[143],"residual":[145],"orbifold":[146],"isotropy":[147],"shown":[149],"have":[151],"degree":[152],"divisible":[153],"least":[156],"common":[157],"multiple":[158],"local":[161],"stabilizer":[162],"orders,":[163],"giving":[164],"arithmetic":[167],"obstruction.":[168]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-04T00:00:00"}