{"id":"https://openalex.org/W7212295258","doi":"https://doi.org/10.48550/arxiv.2609.11627","title":"Bounded vertical deviations and irrational circle factors in Dehn Twist classes","display_name":"Bounded vertical deviations and irrational circle factors in Dehn Twist classes","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212295258","doi":"https://doi.org/10.48550/arxiv.2609.11627"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.11627","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11627","pdf_url":"https://arxiv.org/pdf/2609.11627","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/2609.11627","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151336084","display_name":"Heric Corr\u00eaa","orcid":"https://orcid.org/0000-0002-3911-8386","observed_orcids":["https://orcid.org/0000-0002-3911-8386"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Corr\u00eaa, Heric","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059691044","display_name":"Alejandro Kocsard","orcid":"https://orcid.org/0000-0003-1914-9043","observed_orcids":["https://orcid.org/0000-0003-1914-9043"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kocsard, Alejandro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9965999722480774,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9965999722480774,"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":0.0012000000569969416,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.00019999999494757503,"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/dehn-twists","display_name":"Dehn twists","score":0.7620000243186951},{"id":"https://openalex.org/keywords/topological-extensions","display_name":"topological extensions","score":0.7699999809265137},{"id":"https://openalex.org/keywords/wandering-domains","display_name":"wandering domains","score":0.7059999704360962},{"id":"https://openalex.org/keywords/homotopy-classes","display_name":"homotopy classes","score":0.6790000200271606}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8659999966621399},{"id":"https://openalex.org/C94931360","wikidata":"https://www.wikidata.org/wiki/Q607728","display_name":"Irrational number","level":2,"score":0.7333999872207642},{"id":"https://openalex.org/C2776196297","wikidata":"https://www.wikidata.org/wiki/Q17138781","display_name":"Twist","level":2,"score":0.7106999754905701},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6690999865531921},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.5443999767303467},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.5368000268936157},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4616999924182892},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4392000138759613},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43479999899864197},{"id":"https://openalex.org/C10728891","wikidata":"https://www.wikidata.org/wiki/Q584521","display_name":"Homeomorphism (graph theory)","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28209999203681946},{"id":"https://openalex.org/C35234519","wikidata":"https://www.wikidata.org/wiki/Q3983973","display_name":"Homotopy lifting property","level":4,"score":0.26759999990463257},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2558000087738037},{"id":"https://openalex.org/C135007989","wikidata":"https://www.wikidata.org/wiki/Q643156","display_name":"Rotation number","level":3,"score":0.2524000108242035}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.11627","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11627","pdf_url":"https://arxiv.org/pdf/2609.11627","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.2609.11627","doi":"https://doi.org/10.48550/arxiv.2609.11627","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.11627","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:2609.11627","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11627","pdf_url":"https://arxiv.org/pdf/2609.11627","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/W7212295258.pdf","grobid_xml":"https://content.openalex.org/works/W7212295258.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7120277205","https://openalex.org/W7213878332","https://openalex.org/W2119925874","https://openalex.org/W7221031676","https://openalex.org/W3040486757","https://openalex.org/W2963807075","https://openalex.org/W2968131491","https://openalex.org/W3013853039","https://openalex.org/W7098964805","https://openalex.org/W2038656237"],"abstract_inverted_index":{"We":[0,70],"prove":[1,108],"that":[2,72,109],"a":[3,9,15,33,84,116,138,143],"homeomorphism":[4,39],"of":[5,18,66,103,131],"the":[6,38,46,56,64,67,79,88,92,100,104,110,124,132],"two-torus":[7],"in":[8,45,99,137],"Dehn":[10,85],"twist":[11,86],"homotopy":[12,101],"class":[13,102],"is":[14,112,120,135,141,147],"topological":[16],"extension":[17],"an":[19,60],"irrational":[20,35],"circle":[21,117],"rotation":[22,29,118],"if":[23,26],"and":[24,37,119,146],"only":[25],"its":[27],"vertical":[28,47],"set":[30,134],"reduces":[31],"to":[32,83,115],"single":[34,139],"number":[36],"exhibits":[40],"uniformly":[41],"bounded":[42],"rotational":[43],"deviations":[44],"direction.":[48],"This":[49],"result":[50],"has":[51],"been":[52],"previously":[53],"obtained":[54],"by":[55],"second":[57],"author":[58],"under":[59],"additional":[61],"hypothesis":[62,74],"about":[63],"geometry":[65],"non-wandering":[68],"set.":[69,126],"show":[71],"this":[73],"can":[75],"be":[76,97],"entirely":[77],"dropped:":[78],"large-scale":[80],"shear":[81],"intrinsic":[82],"eliminates":[87],"obstructions":[89],"coming":[90],"from":[91],"wandering":[93,125,133,144],"set,":[94],"which":[95],"cannot":[96],"removed":[98],"identity.":[105],"Finally,":[106],"we":[107],"factor":[111],"unique":[113],"up":[114],"locally":[121],"constant":[122],"on":[123],"Consequently,":[127],"every":[128],"connected":[129],"component":[130],"contained":[136],"fiber,":[140],"itself":[142],"domain":[145],"either":[148],"inessential":[149],"or":[150],"annular.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-12T00:00:00"}
