Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W1480611223', 'doi': None, 'title': 'Strong Rigidity of Locally Symmetric Spaces.', 'display_name': 'Strong Rigidity of Locally Symmetric Spaces.', 'publication_year': 1973, 'publication_date': '1973-12-21', 'ids': {'openalex': 'https://openalex.org/W1480611223', 'mag': '1480611223'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'http://ci.nii.ac.jp/ncid/BA61481711', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'book', 'type_crossref': 'book', 'indexed_in': [], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5087984324', 'display_name': 'G. D. Mostow', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': True, 'raw_author_name': 'George D. Mostow', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': ['https://openalex.org/A5087984324'], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 1.3, 'has_fulltext': False, 'cited_by_count': 897, 'citation_normalized_percentile': {'value': 0.785714, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 99, 'max': 100}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10849', 'display_name': 'Study of Finite Groups and Graphs', 'score': 0.9834, 'subfield': {'id': 'https://openalex.org/subfields/2607', 'display_name': 'Discrete Mathematics and Combinatorics'}, '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/T10849', 'display_name': 'Study of Finite Groups and Graphs', 'score': 0.9834, 'subfield': {'id': 'https://openalex.org/subfields/2607', 'display_name': 'Discrete Mathematics and Combinatorics'}, '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/T11822', 'display_name': 'Geometric Function Theory and Complex Analysis', 'score': 0.9557, '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': 'Symplectic Topology and Knot Invariants', 'score': 0.9137, '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/quasiconformal-mappings', 'display_name': 'Quasiconformal Mappings', 'score': 0.533015}, {'id': 'https://openalex.org/keywords/distance-regular-graphs', 'display_name': 'Distance-Regular Graphs', 'score': 0.532922}, {'id': 'https://openalex.org/keywords/contact-geometry', 'display_name': 'Contact Geometry', 'score': 0.532905}, {'id': 'https://openalex.org/keywords/hypergeometric-functions', 'display_name': 'Hypergeometric Functions', 'score': 0.530036}, {'id': 'https://openalex.org/keywords/conformal-mapping', 'display_name': 'Conformal Mapping', 'score': 0.525505}, {'id': 'https://openalex.org/keywords/rigidity', 'display_name': 'Rigidity (electromagnetism)', 'score': 0.5101929}, {'id': 'https://openalex.org/keywords/rank', 'display_name': 'Rank (graph theory)', 'score': 0.42499617}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.78541327}, {'id': 'https://openalex.org/C62354387', 'wikidata': 'https://www.wikidata.org/wiki/Q875399', 'display_name': 'Boundary (topology)', 'level': 2, 'score': 0.54354954}, {'id': 'https://openalex.org/C160343418', 'wikidata': 'https://www.wikidata.org/wiki/Q185256', 'display_name': 'Rigidity (electromagnetism)', 'level': 2, 'score': 0.5101929}, {'id': 'https://openalex.org/C167204820', 'wikidata': 'https://www.wikidata.org/wiki/Q912058', 'display_name': 'Simply connected space', 'level': 2, 'score': 0.4685921}, {'id': 'https://openalex.org/C9376300', 'wikidata': 'https://www.wikidata.org/wiki/Q168817', 'display_name': 'Algebraic number', 'level': 2, 'score': 0.44138306}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.43137366}, {'id': 'https://openalex.org/C164226766', 'wikidata': 'https://www.wikidata.org/wiki/Q7293202', 'display_name': 'Rank (graph theory)', 'level': 2, 'score': 0.42499617}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.39893207}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.34363723}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.17498809}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.07565412}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'http://ci.nii.ac.jp/ncid/BA61481711', 'pdf_url': None, 'source': None, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [{'display_name': 'Reduced inequalities', 'id': 'https://metadata.un.org/sdg/10', 'score': 0.41}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W3212292137', 'https://openalex.org/W2566412846', 'https://openalex.org/W2317588510', 'https://openalex.org/W2314781788', 'https://openalex.org/W2169194620', 'https://openalex.org/W2134086356', 'https://openalex.org/W2112861192', 'https://openalex.org/W2085585078', 'https://openalex.org/W2079500737', 'https://openalex.org/W2070474672', 'https://openalex.org/W2063094738', 'https://openalex.org/W2044720368', 'https://openalex.org/W2032868343', 'https://openalex.org/W2020029703', 'https://openalex.org/W2012722396', 'https://openalex.org/W1993767762', 'https://openalex.org/W1983894121', 'https://openalex.org/W1565171775', 'https://openalex.org/W1533061882', 'https://openalex.org/W1530501787'], 'abstract_inverted_index': {'*Frontmatter,': [0], 'pg.': [1, 3, 7, 12, 21, 31, 36, 42, 49, 57, 65, 77, 86, 96, 102, 108, 115, 120, 128, 136, 143, 149, 163, 170, 178, 183, 185, 187], 'i*Contents,': [2], 'v*': [4], '1.': [5], 'Introduction,': [6], '1*': [8], '2.': [9], 'Algebraic': [10], 'Preliminaries,': [11, 20], '10*': [13], '3.': [14], 'The': [15, 99, 105, 111, 131, 146, 166], 'Geometry': [16, 45], 'of': [17, 27, 46, 54, 62, 70, 91, 140, 168], 'chi': [18], ':': [19], '20*': [22], '4.': [23], 'A': [24, 39], 'Metric': [25], 'Definition': [26], 'the': [28], 'Maximal': [29], 'Boundary,': [30], '31*': [32], '5.': [33], 'Polar': [34, 80], 'Parts,': [35], '35*': [37], '6.': [38], 'Basic': [40, 100], 'Inequality,': [41], '44*': [43], '7.': [44], 'Neighboring': [47], 'Flats,': [48], '52*': [50], '8.': [51, 59], 'Density': [52, 60], 'Properties': [53, 61], 'Discrete': [55, 63], 'Subgroups,': [56, 64], '62*': [58], '66*': [66], '10.': [67], 'Pseudo': [68], 'Isometries': [69], 'Simply': [71], 'Connected': [72], 'Spaces': [73, 139], 'with': [74], 'Negative': [75], 'Curvature,': [76], '71*': [78], '11.': [79], 'Regular': [81], 'Elements': [82], 'in': [83], 'Co-Compact': [84], 'GAMMA,': [85], '76*': [87], '12.': [88], 'Pseudo-Isometric': [89], 'Invariance': [90], 'Semi-Simple': [92], 'and': [93, 156], 'Unipotent': [94], 'Elements,': [95], '80*': [97], '13.': [98], 'Approximation,': [101], '96*': [103], '14.': [104], 'Map': [106, 113], ',': [107], '103*': [109], '15.': [110], 'Boundary': [112, 147], '0,': [114], '107*': [116], '16.': [117], 'Tits': [118], 'Geometries,': [119], '120*': [121], '17.': [122], 'Rigidity': [123, 175], 'for': [124], 'R-rank': [125, 141], '>': [126], '1,': [127, 142], '125*': [129], '18.': [130], 'Restriction': [132], 'to': [133], 'Simple': [134], 'Groups,': [135], '128*': [137], '19.': [138], '134*': [144], '20.': [145], 'Semi-Metric,': [148], '142*': [150], '21.': [151], 'Quasi-Conformal': [152], 'Mappings': [153], 'Over': [154], 'K': [155], 'Absolute': [157], 'Continuity': [158], 'on': [159], 'Almost': [160], 'All': [161], 'R-Circles,': [162], '156*': [164], '22.': [165], 'Effect': [167], 'Ergodicity,': [169], '169*': [171], '23.': [172], 'R-Rank': [173], '1': [174], 'Proof': [176], 'Concluded,': [177], '180*': [179], '24.': [180], 'Concluding': [181], 'Remarks,': [182], '187*Bibliography,': [184], '193*Backmatter,': [186], '197': [188]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1480611223', 'counts_by_year': [{'year': 2024, 'cited_by_count': 8}, {'year': 2023, 'cited_by_count': 10}, {'year': 2022, 'cited_by_count': 8}, {'year': 2021, 'cited_by_count': 10}, {'year': 2020, 'cited_by_count': 18}, {'year': 2019, 'cited_by_count': 20}, {'year': 2018, 'cited_by_count': 27}, {'year': 2017, 'cited_by_count': 35}, {'year': 2016, 'cited_by_count': 26}, {'year': 2015, 'cited_by_count': 38}, {'year': 2014, 'cited_by_count': 32}, {'year': 2013, 'cited_by_count': 27}, {'year': 2012, 'cited_by_count': 24}], 'updated_date': '2024-09-18T16:16:44.367467', 'created_date': '2016-06-24'}