On cohomological obstructions to the existence of log symplectic structures

Name: Work Video:
Duration: 3 min 30 s
Description: We prove that a compact log symplectic manifold has a class in the second cohomology group whose powers, except maybe for the top, are nontrivial. This result gives cohomological obstructions for the existence of b-log symplectic structures similar to those in symplectic geometry.
Ioan Mărcuţ; Boris Osorno Torres
{'id': 'https://openalex.org/W4301694287', 'doi': 'https://doi.org/10.48550/arxiv.1303.6246', 'title': 'On cohomological obstructions to the existence of log symplectic structures', 'display_name': 'On cohomological obstructions to the existence of log symplectic structures', 'publication_year': 2013, 'publication_date': '2013-01-01', 'ids': {'openalex': 'https://openalex.org/W4301694287', 'doi': 'https://doi.org/10.48550/arxiv.1303.6246'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1303.6246', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': ['arxiv', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/abs/1303.6246', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5049077455', 'display_name': 'Ioan Mărcuţ', 'orcid': 'https://orcid.org/0000-0001-9446-0216'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Marcut, Ioan', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5010629018', 'display_name': 'Boris Osorno Torres', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Torres, Boris Osorno', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 65}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10304', 'display_name': 'Geometric and Algebraic Topology', 'score': 0.9998, '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': 0.9998, '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/T12351', 'display_name': 'Geometry and complex manifolds', 'score': 0.9994, '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': 0.9941, '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/manifold', 'display_name': 'Manifold (fluid mechanics)', 'score': 0.4498566}, {'id': 'https://openalex.org/keywords/symplectomorphism', 'display_name': 'Symplectomorphism', 'score': 0.42624605}], 'concepts': [{'id': 'https://openalex.org/C168619227', 'wikidata': 'https://www.wikidata.org/wiki/Q2190991', 'display_name': 'Symplectic geometry', 'level': 2, 'score': 0.9323294}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.731434}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.6979122}, {'id': 'https://openalex.org/C78606066', 'wikidata': 'https://www.wikidata.org/wiki/Q1198376', 'display_name': 'Cohomology', 'level': 2, 'score': 0.6525855}, {'id': 'https://openalex.org/C2777212361', 'wikidata': 'https://www.wikidata.org/wiki/Q5127848', 'display_name': 'Class (philosophy)', 'level': 2, 'score': 0.5778569}, {'id': 'https://openalex.org/C130190758', 'wikidata': 'https://www.wikidata.org/wiki/Q1064500', 'display_name': 'Symplectic manifold', 'level': 3, 'score': 0.56952393}, {'id': 'https://openalex.org/C136660716', 'wikidata': 'https://www.wikidata.org/wiki/Q7269022', 'display_name': 'Quantum cohomology', 'level': 4, 'score': 0.5095251}, {'id': 'https://openalex.org/C104586451', 'wikidata': 'https://www.wikidata.org/wiki/Q771008', 'display_name': 'Symplectic representation', 'level': 4, 'score': 0.5056467}, {'id': 'https://openalex.org/C529865628', 'wikidata': 'https://www.wikidata.org/wiki/Q1790740', 'display_name': 'Manifold (fluid mechanics)', 'level': 2, 'score': 0.4498566}, {'id': 'https://openalex.org/C2781311116', 'wikidata': 'https://www.wikidata.org/wiki/Q83306', 'display_name': 'Group (periodic table)', 'level': 2, 'score': 0.42937306}, {'id': 'https://openalex.org/C135661100', 'wikidata': 'https://www.wikidata.org/wiki/Q1049064', 'display_name': 'Symplectomorphism', 'level': 3, 'score': 0.42624605}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.36047652}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.13883966}, {'id': 'https://openalex.org/C72738302', 'wikidata': 'https://www.wikidata.org/wiki/Q5384738', 'display_name': 'Equivariant cohomology', 'level': 3, 'score': 0.11649507}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.11553338}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.047167182}, {'id': 'https://openalex.org/C127413603', 'wikidata': 'https://www.wikidata.org/wiki/Q11023', 'display_name': 'Engineering', 'level': 0, 'score': 0.035493016}, {'id': 'https://openalex.org/C78519656', 'wikidata': 'https://www.wikidata.org/wiki/Q101333', 'display_name': 'Mechanical engineering', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C154945302', 'wikidata': 'https://www.wikidata.org/wiki/Q11660', 'display_name': 'Artificial intelligence', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 4, 'locations': [{'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1303.6246', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/1303.6246', 'pdf_url': 'http://arxiv.org/pdf/1303.6246', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://projecteuclid.org/euclid.jsg/1433196064', 'pdf_url': 'https://projecteuclid.org/journals/journal-of-symplectic-geometry/volume-12/issue-4/On-cohomological-obstructions-for-the-existence-of-log-symplectic-structures/jsg/1433196064.pdf', 'source': {'id': 'https://openalex.org/S4306400787', 'display_name': 'Project Euclid (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.1303.6246', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1303.6246', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, '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': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [{'score': 0.53, 'id': 'https://metadata.un.org/sdg/10', 'display_name': 'Reduced inequalities'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W4300938089', 'https://openalex.org/W4298327315', 'https://openalex.org/W4281915249', 'https://openalex.org/W4232459995', 'https://openalex.org/W2997833365', 'https://openalex.org/W2950340291', 'https://openalex.org/W1984102342', 'https://openalex.org/W1983133745', 'https://openalex.org/W1776238081', 'https://openalex.org/W1522140001'], 'abstract_inverted_index': {'We': [0], 'prove': [1], 'that': [2], 'a': [3, 9], 'compact': [4], 'log': [5], 'symplectic': [6, 35, 41], 'manifold': [7], 'has': [8], 'class': [10], 'in': [11, 40], 'the': [12, 21, 31], 'second': [13], 'cohomology': [14], 'group': [15], 'whose': [16], 'powers,': [17], 'except': [18], 'maybe': [19], 'for': [20, 30], 'top,': [22], 'are': [23], 'nontrivial.': [24], 'This': [25], 'result': [26], 'gives': [27], 'cohomological': [28], 'obstructions': [29], 'existence': [32], 'of': [33], 'b-log': [34], 'structures': [36], 'similar': [37], 'to': [38], 'those': [39], 'geometry.': [42]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4301694287', 'counts_by_year': [], 'updated_date': '2024-12-13T07:12:36.426474', 'created_date': '2022-10-05'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
