{"id":"https://openalex.org/W1983033166","doi":"https://doi.org/10.1007/978-1-4757-3951-0","title":"Differential Forms in Algebraic Topology","display_name":"Differential Forms in Algebraic Topology","publication_year":1982,"publication_date":"1982-01-01","ids":{"openalex":"https://openalex.org/W1983033166","doi":"https://doi.org/10.1007/978-1-4757-3951-0","mag":"1983033166"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4757-3951-0","doi":"https://doi.org/10.1007/978-1-4757-3951-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4757-3951-0","pdf_url":null,"source":{"id":"https://openalex.org/S4210201401","display_name":"Graduate texts in mathematics","issn_l":"0072-5285","issn":["0072-5285","2197-5612"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graduate Texts in Mathematics","raw_type":"book"},"volume":null,"type":"book","is_traditional":true,"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/A5112075885","display_name":"Raoul Bott","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]},{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"id":"https://openalex.org/I16269868","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447","country_code":"US","type":"education","lineage":["https://openalex.org/I16269868"]},{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]},{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Raoul Bott","raw_affiliation_strings":["Department of Mathematics Michigan State University East Lansing, MI 48824 95053 USA","Department of Mathematics Santa Clara University Santa Clara, CA","Department of Mathematics Tufts University Medford, MA 02155-7049 USA","Department of Mathematics University of Michigan Ann Arbor, MI 48109 USA","Mathematics Department Harvard University Cambridge, MA 02138-2901 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Michigan State University East Lansing, MI 48824 95053 USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Mathematics Santa Clara University Santa Clara, CA","institution_ids":["https://openalex.org/I16269868"]},{"raw_affiliation_string":"Department of Mathematics Tufts University Medford, MA 02155-7049 USA","institution_ids":["https://openalex.org/I121934306"]},{"raw_affiliation_string":"Department of Mathematics University of Michigan Ann Arbor, MI 48109 USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Mathematics Department Harvard University Cambridge, MA 02138-2901 USA","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053473115","display_name":"Loring W. Tu","orcid":"https://orcid.org/0000-0001-5508-9215","observed_orcids":["https://orcid.org/0000-0001-5508-9215"]},"institutions":[{"id":"https://openalex.org/I121934306","display_name":"Tufts University","ror":"https://ror.org/05wvpxv85","country_code":"US","type":"education","lineage":["https://openalex.org/I121934306"]},{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"id":"https://openalex.org/I16269868","display_name":"Santa Clara University","ror":"https://ror.org/03ypqe447","country_code":"US","type":"education","lineage":["https://openalex.org/I16269868"]},{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]},{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Loring W. Tu","raw_affiliation_strings":["Department of Mathematics Michigan State University East Lansing, MI 48824 95053 USA","Department of Mathematics Santa Clara University Santa Clara, CA","Department of Mathematics Tufts University Medford, MA 02155-7049 USA","Department of Mathematics University of Michigan Ann Arbor, MI 48109 USA","Mathematics Department Harvard University Cambridge, MA 02138-2901 USA"],"raw_orcid":"https://orcid.org/0000-0001-5508-9215","affiliations":[{"raw_affiliation_string":"Department of Mathematics Michigan State University East Lansing, MI 48824 95053 USA","institution_ids":["https://openalex.org/I87216513"]},{"raw_affiliation_string":"Department of Mathematics Santa Clara University Santa Clara, CA","institution_ids":["https://openalex.org/I16269868"]},{"raw_affiliation_string":"Department of Mathematics Tufts University Medford, MA 02155-7049 USA","institution_ids":["https://openalex.org/I121934306"]},{"raw_affiliation_string":"Department of Mathematics University of Michigan Ann Arbor, MI 48109 USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Mathematics Department Harvard University Cambridge, MA 02138-2901 USA","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1876,"has_fulltext":false,"cited_by_count":2796,"citation_normalized_percentile":{"value":0.95070423,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9916999936103821,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9916999936103821,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.00139999995008111,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0013000000035390258,"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/differential-forms","display_name":"differential forms","score":0.9769999980926514},{"id":"https://openalex.org/keywords/de-rham-theory","display_name":"de Rham theory","score":0.9039999842643738},{"id":"https://openalex.org/keywords/spectral-sequences","display_name":"spectral sequences","score":0.9990000128746033},{"id":"https://openalex.org/keywords/characteristic-classes","display_name":"characteristic classes","score":0.9739999771118164},{"id":"https://openalex.org/keywords/algebraic-topology","display_name":"algebraic topology","score":0.8159999847412109}],"concepts":[{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.634995698928833},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5839146375656128},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5086618065834045},{"id":"https://openalex.org/C145054310","wikidata":"https://www.wikidata.org/wiki/Q212803","display_name":"Algebraic topology","level":3,"score":0.4983088970184326},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4846228063106537},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3542305827140808},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16485363245010376},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11904940009117126},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11602261662483215},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.029559820890426636},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/978-1-4757-3951-0","doi":"https://doi.org/10.1007/978-1-4757-3951-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4757-3951-0","pdf_url":null,"source":{"id":"https://openalex.org/S4210201401","display_name":"Graduate texts in mathematics","issn_l":"0072-5285","issn":["0072-5285","2197-5612"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graduate Texts in Mathematics","raw_type":"book"},{"id":"pmh:oai:aleph.bib-bvb.de:BVB01-006916500","doi":null,"is_oa":false,"landing_page_url":"http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916500&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:cds.cern.ch:1615041","doi":null,"is_oa":false,"landing_page_url":"http://cds.cern.ch/record/1615041","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:katalog.pustaka.unand.ac.id:slims-34836","doi":null,"is_oa":false,"landing_page_url":"http://katalog.pustaka.unand.ac.id//index.php?p=show_detail&id=34836","pdf_url":null,"source":{"id":"https://openalex.org/S4377196922","display_name":"Andalas University Repository (Andalas University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I55892964","host_organization_name":"Andalas University","host_organization_lineage":["https://openalex.org/I55892964"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2496424626","https://openalex.org/W4237428150","https://openalex.org/W6981136148","https://openalex.org/W2492662468","https://openalex.org/W2066930486","https://openalex.org/W7098579633","https://openalex.org/W2108685308","https://openalex.org/W275021609","https://openalex.org/W3127368622","https://openalex.org/W2057708085"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":88},{"year":2025,"cited_by_count":79},{"year":2024,"cited_by_count":92},{"year":2023,"cited_by_count":126},{"year":2022,"cited_by_count":90},{"year":2021,"cited_by_count":90},{"year":2020,"cited_by_count":153},{"year":2019,"cited_by_count":94},{"year":2018,"cited_by_count":91},{"year":2017,"cited_by_count":81},{"year":2016,"cited_by_count":94},{"year":2015,"cited_by_count":80},{"year":2014,"cited_by_count":100},{"year":2013,"cited_by_count":85},{"year":2012,"cited_by_count":79}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}