Intersection cohomology of $S^1$ symplectic quotients and small resolutions

Name: Work Video:
Duration: 3 min 30 s
Description: We provided two explicit formulas for the intersection cohomology (as a graded vector space with pairing) of the symplectic quotient by a circle in terms of the $S^1$ equivariant cohomology of the original symplectic manifold and the fixed point data. The key idea is the construction of a small resolution of the symplectic quotient.
Eugene Lerman; Susan Tolman
{'id': 'https://openalex.org/W2950465576', 'doi': 'https://doi.org/10.48550/arxiv.math/9810046', 'title': 'Intersection cohomology of $S^1$ symplectic quotients and small resolutions', 'display_name': 'Intersection cohomology of $S^1$ symplectic quotients and small resolutions', 'publication_year': 1998, 'publication_date': '1998-01-01', 'ids': {'openalex': 'https://openalex.org/W2950465576', 'doi': 'https://doi.org/10.48550/arxiv.math/9810046', 'mag': '2950465576'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/math/9810046', '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': ['datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/abs/math/9810046', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5055475308', 'display_name': 'Eugene Lerman', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Eugene Lerman', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5052244986', 'display_name': 'Susan Tolman', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Susan Tolman', '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': 2, 'citation_normalized_percentile': {'value': 0.62891, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 63, 'max': 67}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10061', 'display_name': 'Algebraic Geometry and Number Theory', 'score': 1.0, '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': 1.0, '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': 0.9999, '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/T11680', 'display_name': 'Advanced Algebra and Geometry', 'score': 0.9998, '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': [], 'concepts': [{'id': 'https://openalex.org/C168619227', 'wikidata': 'https://www.wikidata.org/wiki/Q2190991', 'display_name': 'Symplectic geometry', 'level': 2, 'score': 0.7314499}, {'id': 'https://openalex.org/C64543145', 'wikidata': 'https://www.wikidata.org/wiki/Q162942', 'display_name': 'Intersection (aeronautics)', 'level': 2, 'score': 0.6657124}, {'id': 'https://openalex.org/C199422724', 'wikidata': 'https://www.wikidata.org/wiki/Q41118', 'display_name': 'Quotient', 'level': 2, 'score': 0.633627}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.5938738}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.5563059}, {'id': 'https://openalex.org/C78606066', 'wikidata': 'https://www.wikidata.org/wiki/Q1198376', 'display_name': 'Cohomology', 'level': 2, 'score': 0.5331143}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.33962417}, {'id': 'https://openalex.org/C205649164', 'wikidata': 'https://www.wikidata.org/wiki/Q1071', 'display_name': 'Geography', 'level': 0, 'score': 0.10141221}, {'id': 'https://openalex.org/C58640448', 'wikidata': 'https://www.wikidata.org/wiki/Q42515', 'display_name': 'Cartography', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/math/9810046', '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': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.math/9810046', '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/math/9810046', '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': 0.49, 'id': 'https://metadata.un.org/sdg/10', 'display_name': 'Reduced inequalities'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 10, 'referenced_works': ['https://openalex.org/W1558796308', 'https://openalex.org/W1572740858', 'https://openalex.org/W1831170218', 'https://openalex.org/W1885177267', 'https://openalex.org/W1964141736', 'https://openalex.org/W1983033166', 'https://openalex.org/W1987559245', 'https://openalex.org/W200521721', 'https://openalex.org/W2128559058', 'https://openalex.org/W67977128'], 'related_works': ['https://openalex.org/W4313895414', 'https://openalex.org/W4298064394', 'https://openalex.org/W4292672442', 'https://openalex.org/W2964192738', 'https://openalex.org/W2949502838', 'https://openalex.org/W2791431590', 'https://openalex.org/W2362101859', 'https://openalex.org/W2348909947', 'https://openalex.org/W2027826725', 'https://openalex.org/W139275344'], 'abstract_inverted_index': {'We': [0], 'provided': [1], 'two': [2], 'explicit': [3], 'formulas': [4], 'for': [5], 'the': [6, 17, 26, 31, 36, 44, 51], 'intersection': [7], 'cohomology': [8, 29], '(as': [9], 'a': [10, 21, 47], 'graded': [11], 'vector': [12], 'space': [13], 'with': [14], 'pairing)': [15], 'of': [16, 25, 30, 46, 50], 'symplectic': [18, 33, 52], 'quotient': [19], 'by': [20], 'circle': [22], 'in': [23], 'terms': [24], '$S^1$': [27], 'equivariant': [28], 'original': [32], 'manifold': [34], 'and': [35], 'fixed': [37], 'point': [38], 'data.': [39], 'The': [40], 'key': [41], 'idea': [42], 'is': [43], 'construction': [45], 'small': [48], 'resolution': [49], 'quotient.': [53]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2950465576', 'counts_by_year': [], 'updated_date': '2024-12-17T08:11:35.587578', 'created_date': '2019-06-27'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
