{"id":"https://openalex.org/W7204955104","doi":"https://doi.org/10.48550/arxiv.2608.29046","title":"Fox $p$-Colorings as Fixed Points of Braid Representations","display_name":"Fox $p$-Colorings as Fixed Points of Braid Representations","publication_year":2026,"publication_date":"2026-08-29","ids":{"openalex":"https://openalex.org/W7204955104","doi":"https://doi.org/10.48550/arxiv.2608.29046"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29046","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29046","pdf_url":"https://arxiv.org/pdf/2608.29046","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":null,"license_id":null,"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/2608.29046","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148851814","display_name":"Neungjoo Goh","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I199143407","display_name":"Sunchon National University","ror":"https://ror.org/043jqrs76","country_code":"KR","type":"education","lineage":["https://openalex.org/I199143407"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Goh, Neungjoo","raw_affiliation_strings":["Department of Mathematics Education , Sunchon National University , Sun- chon 57922 , Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education , Sunchon National University , Sun- chon 57922 , Korea","institution_ids":["https://openalex.org/I199143407"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148875805","display_name":"Suah Jeong","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I199143407","display_name":"Sunchon National University","ror":"https://ror.org/043jqrs76","country_code":"KR","type":"education","lineage":["https://openalex.org/I199143407"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jeong, Suah","raw_affiliation_strings":["Department of Mathematics Education , Sunchon National University , Sun- chon 57922 , Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education , Sunchon National University , Sun- chon 57922 , Korea","institution_ids":["https://openalex.org/I199143407"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148861433","display_name":"Seungbin Oh","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I199143407","display_name":"Sunchon National University","ror":"https://ror.org/043jqrs76","country_code":"KR","type":"education","lineage":["https://openalex.org/I199143407"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Oh, Seungbin","raw_affiliation_strings":["Department of Mathematics Education , Sunchon National University , Sun- chon 57922 , Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education , Sunchon National University , Sun- chon 57922 , Korea","institution_ids":["https://openalex.org/I199143407"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087884965","display_name":"Hyungkee Yoo","orcid":"https://orcid.org/0000-0002-6083-3165","observed_orcids":["https://orcid.org/0000-0002-6083-3165"]},"institutions":[{"id":"https://openalex.org/I199143407","display_name":"Sunchon National University","ror":"https://ror.org/043jqrs76","country_code":"KR","type":"education","lineage":["https://openalex.org/I199143407"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Yoo, Hyungkee","raw_affiliation_strings":["Department of Mathematics Education , Sunchon National University , Sun- chon 57922 , Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Education , Sunchon National University , Sun- chon 57922 , Korea","institution_ids":["https://openalex.org/I199143407"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I199143407"],"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":0.9994999766349792,"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":0.9994999766349792,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.0,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/braid-representations","display_name":"braid representations","score":0.8339999914169312},{"id":"https://openalex.org/keywords/fixed-points","display_name":"fixed points","score":0.7160000205039978},{"id":"https://openalex.org/keywords/knot-coloring","display_name":"knot coloring","score":0.6589999794960022},{"id":"https://openalex.org/keywords/links","display_name":"links","score":0.6610000133514404},{"id":"https://openalex.org/keywords/torus-links","display_name":"torus links","score":0.7760000228881836},{"id":"https://openalex.org/keywords/3-coloring","display_name":"3-coloring","score":0.6299999952316284},{"id":"https://openalex.org/keywords/braid-groups","display_name":"braid groups","score":0.47600001096725464}],"concepts":[{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.8752999901771545},{"id":"https://openalex.org/C147441545","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid theory","level":3,"score":0.817300021648407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7967000007629395},{"id":"https://openalex.org/C33840335","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid group","level":2,"score":0.5112000107765198},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.48539999127388},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4803999960422516},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44999998807907104},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.41449999809265137},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3849000036716461},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3792000114917755},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C143330242","wikidata":"https://www.wikidata.org/wiki/Q849798","display_name":"Knot theory","level":3,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29046","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29046","pdf_url":"https://arxiv.org/pdf/2608.29046","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.29046","doi":"https://doi.org/10.48550/arxiv.2608.29046","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29046","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.29046","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29046","pdf_url":"https://arxiv.org/pdf/2608.29046","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204955104.pdf","grobid_xml":"https://content.openalex.org/works/W7204955104.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2108415704","https://openalex.org/W2154839583","https://openalex.org/W2601592395","https://openalex.org/W2145337225","https://openalex.org/W2745115334","https://openalex.org/W1625420124","https://openalex.org/W7097581211","https://openalex.org/W4302362135","https://openalex.org/W4417136687","https://openalex.org/W24729466"],"abstract_inverted_index":{"Fox":[0,31,61,83],"$p$-colorings":[1,32,62],"of":[2,12,33,42,60,63,81],"knots":[3,65],"and":[4,66,75],"links":[5,74],"admit":[6],"a":[7,22,45],"linear-algebraic":[8],"description":[9],"in":[10],"terms":[11],"braid":[13,17,36],"representations.":[14],"For":[15],"each":[16],"$\u03b2\\in":[18],"B_n$":[19],"we":[20],"associate":[21],"representation":[23],"$M":[24],":":[25],"B_n":[26],"\\to":[27],"\\mathrm{GL}(n,\\mathbb{F}_p)$":[28],"such":[29],"that":[30],"the":[34,58,70],"closed":[35],"$\\widehat\u03b2$":[37],"correspond":[38],"to":[39,72],"fixed":[40],"points":[41],"$M(\u03b2)$.":[43],"As":[44],"consequence,":[46],"$$":[47,52],"\\mathrm{Col}_p(\\widehat\u03b2)":[48],"=":[49],"p^{\\dim":[50],"\\ker(M(\u03b2)-I)},":[51],"yielding":[53],"an":[54],"explicit":[55,79],"formula":[56],"for":[57],"number":[59],"arbitrary":[64],"links.":[67],"We":[68],"apply":[69],"method":[71],"torus":[73],"spiral":[76],"links,":[77],"obtaining":[78],"descriptions":[80],"their":[82],"3-coloring":[84],"spaces.":[85]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-02T00:00:00"}
