{"id":"https://openalex.org/W7171950674","doi":"https://doi.org/10.48550/arxiv.2607.27552","title":"Puncture-Forgetting Maps for Measured Foliations and Applications in Teichm\u00fcller Space and Complex Dynamics","display_name":"Puncture-Forgetting Maps for Measured Foliations and Applications in Teichm\u00fcller Space and Complex Dynamics","publication_year":2026,"publication_date":"2026-07-30","ids":{"openalex":"https://openalex.org/W7171950674","doi":"https://doi.org/10.48550/arxiv.2607.27552"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2607.27552","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.27552","pdf_url":"https://arxiv.org/pdf/2607.27552","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/2607.27552","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139408712","display_name":"Jeremy Kahn","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kahn, Jeremy","raw_affiliation_strings":["Department of Mathematics , Brown University , Providence , RI 02912"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Brown University , Providence , RI 02912","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101506508","display_name":"Insung Park","orcid":"https://orcid.org/0000-0001-7710-1297","observed_orcids":["https://orcid.org/0000-0001-7710-1297"]},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]},{"id":"https://openalex.org/I4210087560","display_name":"Stony Brook School","ror":"https://ror.org/003wx9n05","country_code":"US","type":"education","lineage":["https://openalex.org/I4210087560"]},{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Park, Insung","raw_affiliation_strings":["Department of Mathematics , Brown University , Providence , RI 02912","Institute of Mathematical Sciences , Stony Brook University , Stony Brook , NY 11794"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Brown University , Providence , RI 02912","institution_ids":["https://openalex.org/I27804330"]},{"raw_affiliation_string":"Institute of Mathematical Sciences , Stony Brook University , Stony Brook , NY 11794","institution_ids":["https://openalex.org/I4210087560","https://openalex.org/I59553526"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0.8622999787330627,"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":0.8622999787330627,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.12160000205039978,"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/T12504","display_name":"Mathematics and Applications","score":0.0020000000949949026,"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/measured-foliations","display_name":"measured foliations","score":0.9990000128746033},{"id":"https://openalex.org/keywords/teichmuller-space","display_name":"Teichm\u00fcller space","score":0.9110000133514404},{"id":"https://openalex.org/keywords/mapping-class-group","display_name":"mapping class group","score":0.7799999713897705},{"id":"https://openalex.org/keywords/extremal-length","display_name":"extremal length","score":0.9589999914169312},{"id":"https://openalex.org/keywords/cat-0-cube-complexes","display_name":"CAT(0) cube complexes","score":0.9710000157356262},{"id":"https://openalex.org/keywords/horospheres","display_name":"horospheres","score":0.9559999704360962},{"id":"https://openalex.org/keywords/geodesic-flow","display_name":"geodesic flow","score":0.9010000228881836},{"id":"https://openalex.org/keywords/universal-curve","display_name":"universal curve","score":0.9509999752044678}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7017999887466431},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6258999705314636},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6128000020980835},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.5339000225067139},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5205000042915344},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5116000175476074},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4950000047683716},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.49079999327659607},{"id":"https://openalex.org/C154483964","wikidata":"https://www.wikidata.org/wiki/Q825857","display_name":"Riemann sphere","level":3,"score":0.4244999885559082},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.41200000047683716},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38440001010894775},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.3725999891757965},{"id":"https://openalex.org/C162329640","wikidata":"https://www.wikidata.org/wiki/Q332648","display_name":"Covering space","level":2,"score":0.37130001187324524},{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.36820000410079956},{"id":"https://openalex.org/C24129628","wikidata":"https://www.wikidata.org/wiki/Q25345430","display_name":"Complex space","level":3,"score":0.35420000553131104},{"id":"https://openalex.org/C18556879","wikidata":"https://www.wikidata.org/wiki/Q753035","display_name":"Riemann surface","level":2,"score":0.3522999882698059},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3483999967575073},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.3458000123500824},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2937000095844269},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C201661490","wikidata":"https://www.wikidata.org/wiki/Q1774143","display_name":"Cube root","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2607.27552","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.27552","pdf_url":"https://arxiv.org/pdf/2607.27552","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.2607.27552","doi":"https://doi.org/10.48550/arxiv.2607.27552","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.27552","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:2607.27552","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.27552","pdf_url":"https://arxiv.org/pdf/2607.27552","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7171950674.pdf","grobid_xml":"https://content.openalex.org/works/W7171950674.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2937126633","https://openalex.org/W4402857057","https://openalex.org/W4403702451","https://openalex.org/W4416512484","https://openalex.org/W7101678817","https://openalex.org/W7102415478"],"related_works":["https://openalex.org/W2036038950","https://openalex.org/W2196832283","https://openalex.org/W2014050652","https://openalex.org/W4416967220","https://openalex.org/W7098614680","https://openalex.org/W1855197111","https://openalex.org/W7148197585","https://openalex.org/W4289537846","https://openalex.org/W2282362913","https://openalex.org/W4403362693"],"abstract_inverted_index":{"We":[0,71],"introduce":[1],"puncture-forgetting":[2],"maps":[3,51],"for":[4],"measured":[5],"foliations":[6],"and":[7,17,33,82],"investigate":[8],"their":[9],"relations":[10],"with":[11],"mapping":[12],"class":[13],"groups,":[14],"Teichm\u00fcller":[15,90],"spaces,":[16],"extremal":[18],"length.":[19],"To":[20],"this":[21],"end,":[22],"we":[23,56],"develop":[24],"the":[25,45,53,62,86],"notions":[26],"of":[27,30,47],"cube":[28,39],"complexes":[29],"pre-homotopic":[31],"multicurves":[32],"tree":[34],"coordinate":[35],"systems":[36],"on":[37,52],"CAT(0)":[38],"complexes.":[40],"As":[41],"an":[42],"application":[43],"to":[44,76],"dynamics":[46],"post-critically":[48],"finite":[49,63],"rational":[50],"Riemann":[54],"sphere,":[55],"obtain":[57],"a":[58,78],"partial":[59],"result":[60],"toward":[61],"curve":[64,88],"attractor":[65],"conjecture":[66],"posed":[67],"by":[68],"Kevin":[69],"Pilgrim.":[70],"also":[72],"apply":[73],"these":[74],"methods":[75],"uncover":[77],"relation":[79],"between":[80],"horospheres":[81],"geodesic":[83],"flows":[84],"in":[85],"universal":[87],"over":[89],"space.":[91]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-01T00:00:00"}
