{"id":"https://openalex.org/W2796048226","doi":"https://doi.org/10.1007/s00454-022-00400-0","title":"On the Reeb Spaces of Definable Maps","display_name":"On the Reeb Spaces of Definable Maps","publication_year":2022,"publication_date":"2022-07-07","ids":{"openalex":"https://openalex.org/W2796048226","doi":"https://doi.org/10.1007/s00454-022-00400-0","mag":"2796048226"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-022-00400-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-022-00400-0","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057052198","display_name":"Saugata Basu","orcid":"https://orcid.org/0000-0002-2441-0915"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Saugata Basu","raw_affiliation_strings":["Department of Mathematics, Purdue University, West Lafayette, IN, 47906, USA"],"raw_orcid":"https://orcid.org/0000-0002-2441-0915","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, IN, 47906, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090902307","display_name":"Nathanael Cox","orcid":null},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nathanael Cox","raw_affiliation_strings":["Department of Mathematics, Purdue University, West Lafayette, IN, 47906, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, IN, 47906, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040638485","display_name":"Sarah Percival","orcid":null},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sarah Percival","raw_affiliation_strings":["Department of Mathematics, Purdue University, West Lafayette, IN, 47906, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, IN, 47906, USA","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057052198"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.3798,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.46442762,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"68","issue":"2","first_page":"372","last_page":"405"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9997000098228455,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9997000098228455,"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":0.9997000098228455,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9991999864578247,"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/mathematics","display_name":"Mathematics","score":0.9031783938407898},{"id":"https://openalex.org/keywords/betti-number","display_name":"Betti number","score":0.8888858556747437},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.590907633304596},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5659953355789185},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.5638405084609985},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5272171497344971},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5169748067855835},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4507173001766205},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34377405047416687},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.321227490901947},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12935617566108704}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9031783938407898},{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.8888858556747437},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.590907633304596},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5659953355789185},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.5638405084609985},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5272171497344971},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5169748067855835},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4507173001766205},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34377405047416687},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.321227490901947},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12935617566108704},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-022-00400-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-022-00400-0","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5101869891","display_name":null,"funder_award_id":"CCF-1618918","funder_id":"https://openalex.org/F4320332169","funder_display_name":"Directorate for Computer and Information Science and Engineering"},{"id":"https://openalex.org/G7307870410","display_name":null,"funder_award_id":"DMS-1620271","funder_id":"https://openalex.org/F4320332172","funder_display_name":"Directorate for Mathematical and Physical Sciences"}],"funders":[{"id":"https://openalex.org/F4320332169","display_name":"Directorate for Computer and Information Science and Engineering","ror":"https://ror.org/025kzpk63"},{"id":"https://openalex.org/F4320332172","display_name":"Directorate for Mathematical and Physical Sciences","ror":"https://ror.org/029b7h395"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W26023427","https://openalex.org/W126687912","https://openalex.org/W1038888834","https://openalex.org/W1487235877","https://openalex.org/W1493472025","https://openalex.org/W1499561838","https://openalex.org/W1519970706","https://openalex.org/W1592748961","https://openalex.org/W1607787316","https://openalex.org/W1608107556","https://openalex.org/W1822440022","https://openalex.org/W1983183758","https://openalex.org/W1991581432","https://openalex.org/W1996195522","https://openalex.org/W1996643891","https://openalex.org/W2010757891","https://openalex.org/W2071238863","https://openalex.org/W2089472251","https://openalex.org/W2093614095","https://openalex.org/W2119232867","https://openalex.org/W2144905782","https://openalex.org/W2152595409","https://openalex.org/W2159666017","https://openalex.org/W2169785038","https://openalex.org/W2245042828","https://openalex.org/W2503612797","https://openalex.org/W2596464131","https://openalex.org/W2951040153","https://openalex.org/W3102329232","https://openalex.org/W3102754119","https://openalex.org/W3104275909","https://openalex.org/W3106512202","https://openalex.org/W4237293924","https://openalex.org/W4248269519","https://openalex.org/W4255213956","https://openalex.org/W4255383393","https://openalex.org/W4293052550"],"related_works":["https://openalex.org/W1613669816","https://openalex.org/W2995801688","https://openalex.org/W2037918131","https://openalex.org/W4375947497","https://openalex.org/W2963873756","https://openalex.org/W2051103387","https://openalex.org/W2094335718","https://openalex.org/W1995179161","https://openalex.org/W2744298791","https://openalex.org/W1972523355"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}