{"id":"https://openalex.org/W7161586661","doi":"https://doi.org/10.48550/arxiv.2605.15933","title":"A note on short and long exact sequences in the BBG construction of complexes from complexes","display_name":"A note on short and long exact sequences in the BBG construction of complexes from complexes","publication_year":2026,"publication_date":"2026-05-15","ids":{"openalex":"https://openalex.org/W7161586661","doi":"https://doi.org/10.48550/arxiv.2605.15933"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.15933","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15933","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.15933","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136367138","display_name":"Snorre H. Christiansen","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Christiansen, Snorre H.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5136367138"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.3955000042915344,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.3955000042915344,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.2653999924659729,"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"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.05640000104904175,"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/spectral-sequence","display_name":"Spectral sequence","score":0.6722000241279602},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.6664000153541565},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6582000255584717},{"id":"https://openalex.org/keywords/cohomology","display_name":"Cohomology","score":0.6208000183105469},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6158000230789185},{"id":"https://openalex.org/keywords/exact-sequence","display_name":"Exact sequence","score":0.5087000131607056}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7773000001907349},{"id":"https://openalex.org/C178609977","wikidata":"https://www.wikidata.org/wiki/Q3503315","display_name":"Spectral sequence","level":3,"score":0.6722000241279602},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.6664000153541565},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6582000255584717},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.6208000183105469},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6158000230789185},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5325000286102295},{"id":"https://openalex.org/C25534917","wikidata":"https://www.wikidata.org/wiki/Q1326955","display_name":"Exact sequence","level":2,"score":0.5087000131607056},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.3467999994754791},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32910001277923584},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29499998688697815},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.2671999931335449},{"id":"https://openalex.org/C155751095","wikidata":"https://www.wikidata.org/wiki/Q1408937","display_name":"Group cohomology","level":3,"score":0.25780001282691956}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.15933","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15933","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.15933","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.15933","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"score":0.4676482677459717,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"first":[1],"show":[2],"how":[3],"the":[4,15,26,39,45,49],"cohomology":[5,34,65],"of":[6,18,28,41,52,56,64,72],"some":[7],"Bernstein-Gelfand-Gelfand":[8],"(BGG)":[9],"sequences":[10,55,63,74],"that":[11],"are":[12],"important":[13],"for":[14],"numerical":[16],"analysis":[17],"partial":[19],"differential":[20],"equations,":[21],"can":[22],"be":[23],"obtained":[24],"through":[25,48],"construction":[27],"a":[29],"long":[30,61],"exact":[31,54,62],"sequence":[32],"connecting":[33],"groups.":[35,66],"Then":[36],"we":[37],"explain":[38],"extension":[40],"this":[42],"result":[43],"to":[44],"non-injective/surjective":[46],"case":[47],"systematic":[50],"use":[51],"short":[53],"complexes":[57],"and":[58],"their":[59],"associated":[60],"Finally":[67],"an":[68],"interpretation":[69],"in":[70],"terms":[71],"spectral":[73],"is":[75],"given.":[76]},"counts_by_year":[],"updated_date":"2026-05-19T06:20:20.048804","created_date":"2026-05-19T00:00:00"}
