{"id":"https://openalex.org/W7225004957","doi":"https://doi.org/10.5281/zenodo.23826743","title":"Lie group actions and metric criticality in ropelength-filtered knot spaces","display_name":"Lie group actions and metric criticality in ropelength-filtered knot spaces","publication_year":2026,"publication_date":"2026-10-31","ids":{"openalex":"https://openalex.org/W7225004957","doi":"https://doi.org/10.5281/zenodo.23826743"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23826743","doi":"https://doi.org/10.5281/zenodo.23826743","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23826743","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.23826743","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080258413","display_name":"Makoto Ozawa","orcid":"https://orcid.org/0000-0001-7297-0530","observed_orcids":["https://orcid.org/0000-0001-7297-0530"]},"institutions":[{"id":"https://openalex.org/I72956036","display_name":"Komazawa University","ror":"https://ror.org/05tjaf288","country_code":"JP","type":"education","lineage":["https://openalex.org/I72956036"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Ozawa, Makoto","raw_affiliation_strings":["Komazawa University"],"raw_orcid":"https://orcid.org/0000-0001-7297-0530","affiliations":[{"raw_affiliation_string":"Komazawa University","institution_ids":["https://openalex.org/I72956036"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080258413"],"corresponding_institution_ids":["https://openalex.org/I72956036"],"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":0.9955999851226807,"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":0.9955999851226807,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0032999999821186066,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/compact-lie-group-actions","display_name":"compact Lie group actions","score":0.8529999852180481},{"id":"https://openalex.org/keywords/isotropy","display_name":"isotropy","score":0.546999990940094},{"id":"https://openalex.org/keywords/orbit-spaces","display_name":"orbit spaces","score":0.7720000147819519},{"id":"https://openalex.org/keywords/fourier-modes","display_name":"Fourier modes","score":0.7590000033378601},{"id":"https://openalex.org/keywords/symmetry-breaking","display_name":"symmetry breaking","score":0.527999997138977},{"id":"https://openalex.org/keywords/noether-conservation-laws","display_name":"Noether conservation laws","score":0.6169999837875366}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.77920001745224},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.6176000237464905},{"id":"https://openalex.org/C167204820","wikidata":"https://www.wikidata.org/wiki/Q912058","display_name":"Simply connected space","level":2,"score":0.52920001745224},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.524399995803833},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.510699987411499},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4032999873161316},{"id":"https://openalex.org/C131715654","wikidata":"https://www.wikidata.org/wiki/Q288465","display_name":"Group action","level":3,"score":0.3993000090122223},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.38679999113082886},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.38449999690055847},{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.37940001487731934},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.3540000021457672},{"id":"https://openalex.org/C130133044","wikidata":"https://www.wikidata.org/wiki/Q1887083","display_name":"Compact group","level":3,"score":0.3456999957561493},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.3368000090122223},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.31619998812675476},{"id":"https://openalex.org/C133776654","wikidata":"https://www.wikidata.org/wiki/Q2381352","display_name":"Fibered knot","level":2,"score":0.3151000142097473},{"id":"https://openalex.org/C143782950","wikidata":"https://www.wikidata.org/wiki/Q40460","display_name":"Orbifold","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C2780286412","wikidata":"https://www.wikidata.org/wiki/Q1188344","display_name":"Unknot","level":3,"score":0.29580000042915344},{"id":"https://openalex.org/C143330242","wikidata":"https://www.wikidata.org/wiki/Q849798","display_name":"Knot theory","level":3,"score":0.2903999984264374},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.2888000011444092},{"id":"https://openalex.org/C19794929","wikidata":"https://www.wikidata.org/wiki/Q168620","display_name":"Trefoil knot","level":4,"score":0.28690001368522644},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2842999994754791},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.2824000120162964},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26840001344680786},{"id":"https://openalex.org/C50742451","wikidata":"https://www.wikidata.org/wiki/Q1530388","display_name":"Equidistributed sequence","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2635999917984009},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C137618395","wikidata":"https://www.wikidata.org/wiki/Q576728","display_name":"Winding number","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23826743","doi":"https://doi.org/10.5281/zenodo.23826743","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23826743","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.23826744","doi":"https://doi.org/10.5281/zenodo.23826744","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23826744","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.23826743","doi":"https://doi.org/10.5281/zenodo.23826743","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23826743","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/W7221448022","https://openalex.org/W7155055200","https://openalex.org/W2050576778","https://openalex.org/W7162803369","https://openalex.org/W7221799231","https://openalex.org/W2041058517","https://openalex.org/W7221816940","https://openalex.org/W2336742089","https://openalex.org/W7214026060","https://openalex.org/W7100825581"],"abstract_inverted_index":{"We":[0,48,77,222],"examine":[1],"the":[2,5,12,28,43,54,68,83,89,93,100,118,147,159,164,187,196,200,209,211],"role":[3],"of":[4,16,27,30,46,58,67,150,253],"compact":[6,74,259],"Lie":[7],"group":[8,24,85,202],"$SO(3)\\times":[9],"O(2)$":[10],"in":[11,97],"metric":[13],"critical-point":[14],"theory":[15],"normalized":[17,137],"thick":[18,138,151],"knots.":[19],"The":[20],"quotient":[21,165],"by":[22],"this":[23,220],"is":[25,190,216,229],"part":[26],"construction":[29],"ropelength-filtered":[31],"knot":[32,62],"spaces,":[33],"but":[34],"passage":[35],"to":[36,110,193,195],"an":[37],"orbit":[38,119],"space":[39],"need":[40],"not":[41,230],"preserve":[42],"weak-slope":[44,156],"notion":[45],"criticality.":[47],"establish":[49],"elementary":[50],"structural":[51],"results":[52],"for":[53,60,92,136,199,282],"action,":[55],"including":[56,80],"finiteness":[57],"isotropy":[59,173,215],"nontrivial":[61,171],"types":[63],"and":[64,131,162,185,246,250],"exact":[65],"invariance":[66],"descending":[69,233],"strong":[70,234],"slope":[71,95,235],"under":[72],"a":[73,111,122,128,168,206,261,267,283],"isometric":[75],"quotient.":[76],"give":[78],"counterexamples,":[79],"one":[81],"with":[82,127,153,170],"connected":[84,245,255],"$SO(2)$,":[86],"showing":[87],"that":[88,105,177,186,225],"analogous":[90],"assertion":[91],"weak":[94],"fails":[96],"general.":[98],"On":[99],"other":[101],"hand,":[102],"we":[103,132,175,242,273],"prove":[104,251],"it":[106],"does":[107],"hold,":[108],"up":[109,192],"multiplicative":[112],"constant,":[113],"at":[114,167,236],"every":[115],"point":[116],"where":[117],"map":[120],"admits":[121],"Lipschitz":[123],"local":[124],"section":[125],"together":[126],"continuous":[129],"gauge,":[130],"construct":[133],"such":[134],"data":[135],"knots":[139,152],"from":[140,258,278],"finitely":[141,178],"many":[142,179],"Fourier":[143,180],"modes.":[144],"Consequently,":[145],"on":[146,158,163,205],"open":[148],"stratum":[149],"trivial":[154],"isotropy,":[155],"criticality":[157],"parametrized":[160],"model":[161],"coincide;":[166],"configuration":[169],"finite":[172,201,254],"$\\Gamma$":[174,183,203],"show":[176,224],"modes":[181],"recover":[182],"exactly,":[184,265],"comparison":[188],"problem":[189,198],"equivalent,":[191],"constants,":[194],"same":[197],"acting":[204],"slice.":[207],"For":[208,239],"unknot":[210],"round":[212],"circles,":[213],"whose":[214,227],"$O(2)$,":[217],"remain":[218],"outside":[219],"reduction.":[221],"also":[223],"configurations":[226],"thickness":[228],"saturated":[231],"have":[232],"least":[237],"$2\\pi/(\\pi+1)$.":[238],"closed":[240],"subgroups":[241],"define":[243],"symmetry-constrained":[244],"path":[247],"minimax":[248,270],"levels":[249,257],"attainment":[252],"merge":[256],"sublevels;":[260],"finite-dimensional":[262],"example,":[263],"computed":[264],"demonstrates":[266],"strict":[268],"symmetry-breaking":[269],"gap.":[271],"Finally":[272],"distinguish":[274],"these":[275],"static":[276],"statements":[277],"Noether":[279],"conservation":[280],"laws":[281],"separately":[284],"specified":[285],"dynamics.":[286]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-11-01T00:00:00"}