{"id":"https://openalex.org/W3092530310","doi":"https://doi.org/10.1080/10586458.2021.1994059","title":"Cohomology fractals, Cannon\u2013Thurston maps, and the geodesic flow","display_name":"Cohomology fractals, Cannon\u2013Thurston maps, and the geodesic flow","publication_year":2022,"publication_date":"2022-09-15","ids":{"openalex":"https://openalex.org/W3092530310","doi":"https://doi.org/10.1080/10586458.2021.1994059","mag":"3092530310"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2021.1994059","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1994059","pdf_url":"https://www.tandfonline.com/doi/epdf/10.1080/10586458.2021.1994059?needAccess=true&role=button","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.tandfonline.com/doi/epdf/10.1080/10586458.2021.1994059?needAccess=true&role=button","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112026214","display_name":"David Bachman","orcid":null},"institutions":[{"id":"https://openalex.org/I141778976","display_name":"Pitzer College","ror":"https://ror.org/0197n2v40","country_code":"US","type":"education","lineage":["https://openalex.org/I141778976"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Bachman","raw_affiliation_strings":["Pitzer College, 1050 N. Mills Ave. Claremont, CA 91711, USA"],"affiliations":[{"raw_affiliation_string":"Pitzer College, 1050 N. Mills Ave. Claremont, CA 91711, USA","institution_ids":["https://openalex.org/I141778976"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086203421","display_name":"Matthias Goerner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matthias Goerner","raw_affiliation_strings":["Pixar Animation Studios, 1200 Park Avenue, Emeryville, CA 94608, USA"],"affiliations":[{"raw_affiliation_string":"Pixar Animation Studios, 1200 Park Avenue, Emeryville, CA 94608, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052496150","display_name":"Saul Schleimer","orcid":"https://orcid.org/0000-0003-3362-7822"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Saul Schleimer","raw_affiliation_strings":["Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058246509","display_name":"Henry Segerman","orcid":"https://orcid.org/0000-0002-4532-3095"},"institutions":[{"id":"https://openalex.org/I115475287","display_name":"Oklahoma State University","ror":"https://ror.org/01g9vbr38","country_code":"US","type":"education","lineage":["https://openalex.org/I115475287"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Henry Segerman","raw_affiliation_strings":["Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA","institution_ids":["https://openalex.org/I115475287"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5052496150"],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":null,"apc_paid":null,"fwci":0.4019,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.50534308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"4","first_page":"1047","last_page":"1085"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9986000061035156,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8610723614692688},{"id":"https://openalex.org/keywords/cohomology","display_name":"Cohomology","score":0.7747944593429565},{"id":"https://openalex.org/keywords/\u010dech-cohomology","display_name":"\u010cech cohomology","score":0.7002173662185669},{"id":"https://openalex.org/keywords/de-rham-cohomology","display_name":"De Rham cohomology","score":0.5978984236717224},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5056862831115723},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.4903726577758789},{"id":"https://openalex.org/keywords/group-cohomology","display_name":"Group cohomology","score":0.4654354155063629},{"id":"https://openalex.org/keywords/equivariant-cohomology","display_name":"Equivariant cohomology","score":0.3915797472000122},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37308788299560547}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8610723614692688},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.7747944593429565},{"id":"https://openalex.org/C74196217","wikidata":"https://www.wikidata.org/wiki/Q1095535","display_name":"\u010cech cohomology","level":5,"score":0.7002173662185669},{"id":"https://openalex.org/C68365058","wikidata":"https://www.wikidata.org/wiki/Q1179446","display_name":"De Rham cohomology","level":4,"score":0.5978984236717224},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5056862831115723},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.4903726577758789},{"id":"https://openalex.org/C155751095","wikidata":"https://www.wikidata.org/wiki/Q1408937","display_name":"Group cohomology","level":3,"score":0.4654354155063629},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.3915797472000122},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37308788299560547}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.2021.1994059","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1994059","pdf_url":"https://www.tandfonline.com/doi/epdf/10.1080/10586458.2021.1994059?needAccess=true&role=button","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:169515","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:2010.05840","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.05840","pdf_url":"https://arxiv.org/pdf/2010.05840","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.1080/10586458.2021.1994059","is_oa":true,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1994059","pdf_url":"https://www.tandfonline.com/doi/epdf/10.1080/10586458.2021.1994059?needAccess=true&role=button","source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1786514303","display_name":null,"funder_award_id":"DMS-1439786","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2397474635","display_name":"Three- and Four-Dimensional Triangulations and Mathematical Visualization","funder_award_id":"1708239","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3711011437","display_name":null,"funder_award_id":"G-2019-11406","funder_id":"https://openalex.org/F4320306151","funder_display_name":"Alfred P. Sloan Foundation"},{"id":"https://openalex.org/G3963605349","display_name":null,"funder_award_id":"DMS-1708239","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3092530310.pdf","grobid_xml":"https://content.openalex.org/works/W3092530310.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W137235440","https://openalex.org/W1565094355","https://openalex.org/W1967057555","https://openalex.org/W1972545445","https://openalex.org/W1976449906","https://openalex.org/W2011982961","https://openalex.org/W2013390876","https://openalex.org/W2036138621","https://openalex.org/W2042355226","https://openalex.org/W2044720368","https://openalex.org/W2052099954","https://openalex.org/W2068943152","https://openalex.org/W2080671211","https://openalex.org/W2090305144","https://openalex.org/W2096579608","https://openalex.org/W2140307671","https://openalex.org/W2735058722","https://openalex.org/W2941388407","https://openalex.org/W2964268401","https://openalex.org/W2969292053","https://openalex.org/W2972526171","https://openalex.org/W3105997822","https://openalex.org/W3117664331","https://openalex.org/W4230979242","https://openalex.org/W4233597335","https://openalex.org/W4241215102","https://openalex.org/W4242442420","https://openalex.org/W4244277957","https://openalex.org/W4256206838","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1977713768","https://openalex.org/W2624810412","https://openalex.org/W1990583353","https://openalex.org/W3100282197","https://openalex.org/W3032867275","https://openalex.org/W2998916590","https://openalex.org/W2962810052","https://openalex.org/W2732979024","https://openalex.org/W4247441239","https://openalex.org/W4235612579"],"abstract_inverted_index":{"Cohomology":[0],"fractals":[1,35,75,94,112,125],"are":[2,113],"images":[3,15,72],"naturally":[4],"associated":[5],"to":[6,27,38,59,65,76,129],"cohomology":[7,34,55,74,93,111,124,155],"classes":[8],"in":[9,23,132],"hyperbolic":[10,21],"three-manifolds.":[11],"We":[12,32],"generate":[13],"these":[14,51,102],"for":[16],"cusped,":[17],"incomplete,":[18],"and":[19,154],"closed":[20],"three-manifolds":[22],"real-time":[24],"by":[25,69,101],"raytracing":[26],"a":[28,48,60,83,130,142],"fixed":[29],"visual":[30,97],"radius.":[31],"discovered":[33],"while":[36],"attempting":[37],"illustrate":[39],"Cannon-Thurston":[40,80],"maps":[41],"without":[42],"using":[43],"vector":[44],"graphics;":[45],"we":[46,87,104,136],"prove":[47,105],"correspondence":[49],"between":[50],"two,":[52],"when":[53],"the":[54,89,96,107,110,123,133,139,145,152],"class":[56],"is":[57,141],"dual":[58],"fibration.":[61],"This":[62],"allows":[63],"us":[64],"verify":[66],"our":[67,71],"implementations":[68],"comparing":[70],"of":[73,79,85,92,109],"existing":[77],"pictures":[78],"maps.":[81],"In":[82,121],"sequence":[84],"experiments,":[86,103],"explore":[88],"limiting":[90],"behaviour":[91],"as":[95],"radius":[98],"increases.":[99],"Motivated":[100],"that":[106,138],"values":[108],"normally":[114],"distributed,":[115],"but":[116],"with":[117],"diverging":[118],"standard":[119],"deviations.":[120],"fact,":[122],"do":[126],"not":[127],"converge":[128],"function":[131],"limit.":[134],"Instead,":[135],"show":[137],"limit":[140],"distribution":[143],"on":[144,151],"sphere":[146],"at":[147],"infinity,":[148],"only":[149],"depending":[150],"manifold":[153],"class.":[156]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
