The A.P.S. signature formula for measured foliations

Name: Work Video:
Duration: 3 min 30 s
Description: We define the Analytical signature, the Hodge signature and the de Rham signature for a foliated manifold with boundary with foliation transverse to the boundary. We show that all these signatures coincide and a Hirzebruch formula is valid.
Paolo Antonini
{'id': 'https://openalex.org/W1671124163', 'doi': 'https://doi.org/10.48550/arxiv.0907.0801', 'title': 'The A.P.S. signature formula for measured foliations', 'display_name': 'The A.P.S. signature formula for measured foliations', 'publication_year': 2009, 'publication_date': '2009-01-01', 'ids': {'openalex': 'https://openalex.org/W1671124163', 'doi': 'https://doi.org/10.48550/arxiv.0907.0801', 'mag': '1671124163'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/0907.0801', '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/0907.0801', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5079617160', 'display_name': 'Paolo Antonini', 'orcid': 'https://orcid.org/0000-0002-1364-0344'}, 'institutions': [], 'countries': [], 'is_corresponding': True, 'raw_author_name': 'Paolo Antonini', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': ['https://openalex.org/A5079617160'], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 1, 'citation_normalized_percentile': {'value': 0.506122, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 64, 'max': 71}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10899', 'display_name': 'Advanced Operator Algebra Research', 'score': 1.0, '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/T10899', 'display_name': 'Advanced Operator Algebra Research', 'score': 1.0, '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/T10304', 'display_name': 'Geometric and Algebraic Topology', 'score': 0.9996, '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': 0.9988, '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/signature', 'display_name': 'Signature (topology)', 'score': 0.9534303}, {'id': 'https://openalex.org/keywords/foliation', 'display_name': 'Foliation (geology)', 'score': 0.62677693}, {'id': 'https://openalex.org/keywords/manifold', 'display_name': 'Manifold (fluid mechanics)', 'score': 0.6266183}], 'concepts': [{'id': 'https://openalex.org/C2779696439', 'wikidata': 'https://www.wikidata.org/wiki/Q7512811', 'display_name': 'Signature (topology)', 'level': 2, 'score': 0.9534303}, {'id': 'https://openalex.org/C62354387', 'wikidata': 'https://www.wikidata.org/wiki/Q875399', 'display_name': 'Boundary (topology)', 'level': 2, 'score': 0.7621197}, {'id': 'https://openalex.org/C168425004', 'wikidata': 'https://www.wikidata.org/wiki/Q525802', 'display_name': 'Foliation (geology)', 'level': 3, 'score': 0.62677693}, {'id': 'https://openalex.org/C529865628', 'wikidata': 'https://www.wikidata.org/wiki/Q1790740', 'display_name': 'Manifold (fluid mechanics)', 'level': 2, 'score': 0.6266183}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.51235235}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.4206728}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.37425834}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.3037427}, {'id': 'https://openalex.org/C127313418', 'wikidata': 'https://www.wikidata.org/wiki/Q1069', 'display_name': 'Geology', 'level': 0, 'score': 0.22615463}, {'id': 'https://openalex.org/C127413603', 'wikidata': 'https://www.wikidata.org/wiki/Q11023', 'display_name': 'Engineering', 'level': 0, 'score': 0.06908268}, {'id': 'https://openalex.org/C78519656', 'wikidata': 'https://www.wikidata.org/wiki/Q101333', 'display_name': 'Mechanical engineering', 'level': 1, 'score': 0.054867476}, {'id': 'https://openalex.org/C17409809', 'wikidata': 'https://www.wikidata.org/wiki/Q161764', 'display_name': 'Geochemistry', 'level': 1, 'score': 0.044686437}, {'id': 'https://openalex.org/C26687426', 'wikidata': 'https://www.wikidata.org/wiki/Q47069', 'display_name': 'Metamorphic rock', 'level': 2, 'score': 0.0}], 'mesh': [], 'locations_count': 2, 'locations': [{'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/0907.0801', '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.0907.0801', '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/0907.0801', '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': 0.56, 'display_name': 'Life on land', 'id': 'https://metadata.un.org/sdg/15'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 12, 'referenced_works': ['https://openalex.org/W1680579736', 'https://openalex.org/W1868496487', 'https://openalex.org/W1964024648', 'https://openalex.org/W1965791465', 'https://openalex.org/W2017041721', 'https://openalex.org/W2079747489', 'https://openalex.org/W2127494126', 'https://openalex.org/W2516772689', 'https://openalex.org/W2952944690', 'https://openalex.org/W2955546572', 'https://openalex.org/W3104093207', 'https://openalex.org/W633943769'], 'related_works': ['https://openalex.org/W4245975975', 'https://openalex.org/W4220852939', 'https://openalex.org/W3129233334', 'https://openalex.org/W2535453629', 'https://openalex.org/W2054424508', 'https://openalex.org/W1986379449', 'https://openalex.org/W1981480796', 'https://openalex.org/W1976920294', 'https://openalex.org/W1971354599', 'https://openalex.org/W1653893795'], 'abstract_inverted_index': {'We': [0, 25], 'define': [1], 'the': [2, 5, 9, 23], 'Analytical': [3], 'signature,': [4], 'Hodge': [6], 'signature': [7, 12], 'and': [8, 32], 'de': [10], 'Rham': [11], 'for': [13], 'a': [14, 33], 'foliated': [15], 'manifold': [16], 'with': [17, 19], 'boundary': [18], 'foliation': [20], 'transverse': [21], 'to': [22], 'boundary.': [24], 'show': [26], 'that': [27], 'all': [28], 'these': [29], 'signatures': [30], 'coincide': [31], 'Hirzebruch': [34], 'formula': [35], 'is': [36], 'valid.': [37]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1671124163', 'counts_by_year': [], 'updated_date': '2024-12-13T05:54:15.572613', 'created_date': '2016-06-24'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
