{"id":"https://openalex.org/W7163031922","doi":"https://doi.org/10.48550/arxiv.2605.30799","title":"Remarks about the Moebius-Kantor graph","display_name":"Remarks about the Moebius-Kantor graph","publication_year":2026,"publication_date":"2026-05-29","ids":{"openalex":"https://openalex.org/W7163031922","doi":"https://doi.org/10.48550/arxiv.2605.30799"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.30799","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30799","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,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.30799","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082554988","display_name":"Oliver Knill","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Knill, Oliver","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5082554988"],"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.5691999793052673,"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":0.5691999793052673,"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/T10849","display_name":"Finite Group Theory Research","score":0.1298999935388565,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.10300000011920929,"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/dihedral-group","display_name":"Dihedral group","score":0.6621999740600586},{"id":"https://openalex.org/keywords/coxeter-group","display_name":"Coxeter group","score":0.4902999997138977},{"id":"https://openalex.org/keywords/dual-graph","display_name":"Dual graph","score":0.4869999885559082},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.4153999984264374},{"id":"https://openalex.org/keywords/quaternion-group","display_name":"Quaternion group","score":0.41370001435279846},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.38679999113082886},{"id":"https://openalex.org/keywords/point-group","display_name":"Point group","score":0.3847000002861023},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3815999925136566},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.376800000667572}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7651000022888184},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6930999755859375},{"id":"https://openalex.org/C72409365","wikidata":"https://www.wikidata.org/wiki/Q558339","display_name":"Dihedral group","level":3,"score":0.6621999740600586},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49900001287460327},{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.4902999997138977},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.4869999885559082},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.4153999984264374},{"id":"https://openalex.org/C48756202","wikidata":"https://www.wikidata.org/wiki/Q1335680","display_name":"Quaternion group","level":4,"score":0.41370001435279846},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.38679999113082886},{"id":"https://openalex.org/C57796230","wikidata":"https://www.wikidata.org/wiki/Q899720","display_name":"Point group","level":2,"score":0.3847000002861023},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3815999925136566},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.376800000667572},{"id":"https://openalex.org/C140860697","wikidata":"https://www.wikidata.org/wiki/Q5179941","display_name":"Coxeter element","level":3,"score":0.3767000138759613},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.35100001096725464},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3409000039100647},{"id":"https://openalex.org/C170124329","wikidata":"https://www.wikidata.org/wiki/Q592651","display_name":"Non-abelian group","level":4,"score":0.3319000005722046},{"id":"https://openalex.org/C130630368","wikidata":"https://www.wikidata.org/wiki/Q3777914","display_name":"Dicyclic group","level":5,"score":0.3163999915122986},{"id":"https://openalex.org/C201064014","wikidata":"https://www.wikidata.org/wiki/Q3956993","display_name":"Artin group","level":3,"score":0.3138999938964844},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.3034000098705292},{"id":"https://openalex.org/C206219070","wikidata":"https://www.wikidata.org/wiki/Q1755242","display_name":"Nilpotent group","level":3,"score":0.29899999499320984},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.29739999771118164},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2556999921798706},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.2517000138759613},{"id":"https://openalex.org/C200597783","wikidata":"https://www.wikidata.org/wiki/Q4391289","display_name":"Edge-transitive graph","level":5,"score":0.25040000677108765}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.30799","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30799","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,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.30799","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30799","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,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,81],"Moebius-Kantor":[1],"graph":[2,7,32,82],"MK=G(8,3)":[3],"is":[4,69,103],"a":[5,90,104,112],"Cayley":[6],"of":[8,27,40,53,73,77,85,89,106],"three":[9],"non-abelian":[10],"groups,":[11],"the":[12,16,23,36,41,46,50,58,63,71,74,78,94,107,127,131,137,142,148,152],"Pauli":[13,132],"group":[14,18,25,48,52,122,133,144],"P(1),":[15],"semi-dihedral":[17],"SD(16),":[19],"as":[20,22,136],"well":[21],"dihedral":[24,143],"D(16)":[26,145],"order":[28],"16.":[29],"In":[30],"topological":[31],"theory,":[33],"it":[34],"illustrates":[35],"Heawood":[37],"number":[38],"7":[39],"torus":[42],"and":[43],"leads":[44],"to":[45,61],"Tucker":[47],"Aut(MK),":[49],"unique":[51],"genus":[54],"2.":[55],"We":[56],"compute":[57],"Lefschetz":[59],"numbers":[60],"illustrate":[62],"Brouwer-Lefschetz":[64],"fixed":[65],"point":[66],"theorem.":[67],"MK":[68,102],"also":[70],"dual":[72],"2-skeleton":[75],"complex":[76],"3-sphere":[79,95],"G.":[80],"represents":[83],"one":[84,120],"flat":[86],"Clifford":[87],"tori":[88],"Hopf":[91],"fibration":[92],"in":[93],"G=K(2,2,2,2)":[96],"reflecting":[97],"that":[98,101,116,125],"Coxeter":[99],"saw":[100],"subgraph":[105],"tesseract":[108],"G*.":[109],"It":[110,129],"carries":[111],"metric":[113,153],"d":[114],"so":[115],"(MK,d)":[117],"has":[118],"only":[119],"algebraic":[121,149],"structure":[123,150],"(P(1),*)":[124],"preserves":[126],"metric.":[128],"makes":[130,141],"natural,":[134,146],"similarly":[135],"Moebius":[138],"ladder":[139],"M(16)":[140],"forcing":[147],"from":[151],"structure.":[154]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-02T00:00:00"}
