{"id":"https://openalex.org/W4411141177","doi":"https://doi.org/10.1090/mcom/4113","title":"The Diophantine problem in Thompson\u2019s group \ud835\udc39","display_name":"The Diophantine problem in Thompson\u2019s group \ud835\udc39","publication_year":2025,"publication_date":"2025-06-09","ids":{"openalex":"https://openalex.org/W4411141177","doi":"https://doi.org/10.1090/mcom/4113"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/4113","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4113","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2502.14970","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113643512","display_name":"Luna Elliott","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Luna Elliott","raw_affiliation_strings":["Department of Mathematics, University of Manchester, Alan Turing Building, Oxford Rd, Manchester, M13 9PL, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manchester, Alan Turing Building, Oxford Rd, Manchester, M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083566469","display_name":"Alex Levine","orcid":"https://orcid.org/0000-0001-9633-9313"},"institutions":[{"id":"https://openalex.org/I1118541","display_name":"University of East Anglia","ror":"https://ror.org/026k5mg93","country_code":"GB","type":"education","lineage":["https://openalex.org/I1118541"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alex Levine","raw_affiliation_strings":["School of Engineering, Mathematics and Physics, University of East Anglia, Norwich Research Park, Norwich, Norfolk, NR4 7TJ, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering, Mathematics and Physics, University of East Anglia, Norwich Research Park, Norwich, Norfolk, NR4 7TJ, UK","institution_ids":["https://openalex.org/I1118541"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17406798,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"360","first_page":"2013","last_page":"2023"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994000196456909,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9019460678100586},{"id":"https://openalex.org/keywords/diophantine-equation","display_name":"Diophantine equation","score":0.8326968550682068},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6002565622329712},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38285279273986816},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3624383807182312},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3538530766963959},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3312034010887146}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9019460678100586},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.8326968550682068},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6002565622329712},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38285279273986816},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3624383807182312},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3538530766963959},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3312034010887146},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/4113","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4113","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2502.14970","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2502.14970","pdf_url":"https://arxiv.org/pdf/2502.14970","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,"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":"pmh:oai:arXiv.org:2502.14970","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2502.14970","pdf_url":"https://arxiv.org/pdf/2502.14970","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,"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":[],"awards":[{"id":"https://openalex.org/G8107734586","display_name":"Algorithmic, topological and geometric aspects of infinite groups, monoids and inverse semigroups","funder_award_id":"EP/V032003/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411141177.pdf","grobid_xml":"https://content.openalex.org/works/W4411141177.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1509877054","https://openalex.org/W1606202023","https://openalex.org/W1807342037","https://openalex.org/W1965938273","https://openalex.org/W1984884268","https://openalex.org/W1993173561","https://openalex.org/W1993370765","https://openalex.org/W1993909257","https://openalex.org/W2032367968","https://openalex.org/W2038905684","https://openalex.org/W2040480652","https://openalex.org/W2068714254","https://openalex.org/W2078463686","https://openalex.org/W2093596473","https://openalex.org/W2107311001","https://openalex.org/W2118240797","https://openalex.org/W2126039214","https://openalex.org/W2129564013","https://openalex.org/W2166461033","https://openalex.org/W2290050901","https://openalex.org/W2766154976","https://openalex.org/W2797124064","https://openalex.org/W2805792081","https://openalex.org/W2953023563","https://openalex.org/W2962823911","https://openalex.org/W2962957844","https://openalex.org/W3006408918","https://openalex.org/W3034988853","https://openalex.org/W3093089827","https://openalex.org/W3101690275","https://openalex.org/W3106143264","https://openalex.org/W3116942974","https://openalex.org/W3157128827","https://openalex.org/W4236354959","https://openalex.org/W4239478883","https://openalex.org/W4385552555","https://openalex.org/W4386436362","https://openalex.org/W4399657823","https://openalex.org/W4405185152","https://openalex.org/W4406141752","https://openalex.org/W4408297963","https://openalex.org/W6648519890","https://openalex.org/W6651905153","https://openalex.org/W6670199632","https://openalex.org/W6911209040"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2323172212","https://openalex.org/W1799780713","https://openalex.org/W4323907493","https://openalex.org/W2378613393","https://openalex.org/W4297688629","https://openalex.org/W1550725800","https://openalex.org/W4385711919","https://openalex.org/W2370478068","https://openalex.org/W4384345859"],"abstract_inverted_index":{"We":[0],"show":[1,62],"that":[2,18],"the":[3,16,63],"Diophantine":[4,64],"problem":[5,65],"in":[6,66],"Thompson\u2019s":[7],"group":[8],"F":[9,10,19,20],"is":[11,74],"undecidable.":[12,75],"Our":[13],"proof":[14],"uses":[15,31],"facts":[17],"has":[21],"finite":[22],"commutator":[23],"width":[24],"and":[25,37,48,50,69],"rank":[26],"2":[27,28],"abelianisation,":[29],"then":[30],"similar":[32],"arguments":[33],"used":[34],"by":[35],"B\u00fcchi":[36],"Senger":[38],"[Z.":[39],"Math.":[40,43,53],"Logik":[41],"Grundlag.":[42],"34":[44],"(1988),":[45],"pp.":[46,59],"337\u2013342]":[47],"Ciobanu":[49],"Garreta":[51],"[Int.":[52],"Res.":[54],"Not.":[55],"IMRN":[56],"5":[57],"(2024),":[58],"4119\u20134159]":[60],"to":[61],"free":[67],"groups":[68],"monoids":[70],"with":[71],"abelianisation":[72],"constraints":[73]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}