Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W4297571775', 'doi': 'https://doi.org/10.2140/gt.2005.9.1501', 'title': 'Hadamard spaces with isolated flats, with an appendix written jointly with Mohamad Hindawi', 'display_name': 'Hadamard spaces with isolated flats, with an appendix written jointly with Mohamad Hindawi', 'publication_year': 2005, 'publication_date': '2005-08-08', 'ids': {'openalex': 'https://openalex.org/W4297571775', 'doi': 'https://doi.org/10.2140/gt.2005.9.1501'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.2140/gt.2005.9.1501', 'pdf_url': 'http://msp.org/gt/2005/9-3/gt-v9-n3-p08-s.pdf', 'source': {'id': 'https://openalex.org/S50220091', 'display_name': 'Geometry & Topology', 'issn_l': '1364-0380', 'issn': ['1364-0380', '1465-3060'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['arxiv', 'crossref', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'http://msp.org/gt/2005/9-3/gt-v9-n3-p08-s.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5078490489', 'display_name': 'G. Christopher Hruska', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I40347166', 'display_name': 'University of Chicago', 'ror': 'https://ror.org/024mw5h28', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I40347166']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'G Christopher Hruska', 'raw_affiliation_strings': ['Department of Mathematics, University of Chicago, 5734 S University Ave, Chicago, Illinois 60637-1514, USA'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, University of Chicago, 5734 S University Ave, Chicago, Illinois 60637-1514, USA', 'institution_ids': ['https://openalex.org/I40347166']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5081969698', 'display_name': 'Bruce Kleiner', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I27837315', 'display_name': 'University of Michigan–Ann Arbor', 'ror': 'https://ror.org/00jmfr291', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I27837315']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Bruce Kleiner', 'raw_affiliation_strings': ['Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109, USA'], 'affiliations': [{'raw_affiliation_string': 'Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109, USA', 'institution_ids': ['https://openalex.org/I27837315']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 3.021, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 54, 'citation_normalized_percentile': {'value': 0.957287, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 93, 'max': 94}, 'biblio': {'volume': '9', 'issue': '3', 'first_page': '1501', 'last_page': '1538'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10304', 'display_name': 'Geometric and Algebraic Topology', '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'}}, 'topics': [{'id': 'https://openalex.org/T10304', 'display_name': 'Geometric and Algebraic Topology', '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/T10899', 'display_name': 'Advanced Operator Algebra Research', 'score': 0.9971, '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/T10896', 'display_name': 'Homotopy and Cohomology in Algebraic Topology', 'score': 0.997, '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/equivariant-map', 'display_name': 'Equivariant map', 'score': 0.6130271}, {'id': 'https://openalex.org/keywords/disjoint-sets', 'display_name': 'Disjoint sets', 'score': 0.50579333}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.83395696}, {'id': 'https://openalex.org/C171036898', 'wikidata': 'https://www.wikidata.org/wiki/Q256355', 'display_name': 'Equivariant map', 'level': 2, 'score': 0.6130271}, {'id': 'https://openalex.org/C62354387', 'wikidata': 'https://www.wikidata.org/wiki/Q875399', 'display_name': 'Boundary (topology)', 'level': 2, 'score': 0.57928395}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.53270406}, {'id': 'https://openalex.org/C12362212', 'wikidata': 'https://www.wikidata.org/wiki/Q728435', 'display_name': 'Linear subspace', 'level': 2, 'score': 0.52087927}, {'id': 'https://openalex.org/C190470478', 'wikidata': 'https://www.wikidata.org/wiki/Q2370229', 'display_name': 'Invariant (physics)', 'level': 2, 'score': 0.50782806}, {'id': 'https://openalex.org/C45340560', 'wikidata': 'https://www.wikidata.org/wiki/Q215382', 'display_name': 'Disjoint sets', 'level': 2, 'score': 0.50579333}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.31724572}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.3070288}, {'id': 'https://openalex.org/C37914503', 'wikidata': 'https://www.wikidata.org/wiki/Q156495', 'display_name': 'Mathematical physics', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 4, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.2140/gt.2005.9.1501', 'pdf_url': 'http://msp.org/gt/2005/9-3/gt-v9-n3-p08-s.pdf', 'source': {'id': 'https://openalex.org/S50220091', 'display_name': 'Geometry & Topology', 'issn_l': '1364-0380', 'issn': ['1364-0380', '1465-3060'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/math/0411232', 'pdf_url': 'http://arxiv.org/pdf/math/0411232', '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': 'https://projecteuclid.org/euclid.gt/1513799642', 'pdf_url': 'https://projecteuclid.org/journals/geometry-and-topology/volume-9/issue-3/Hadamard-spaces-with-isolated-flats-with-an-appendix-written-jointly/10.2140/gt.2005.9.1501.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': '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/0411232', '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://doi.org/10.2140/gt.2005.9.1501', 'pdf_url': 'http://msp.org/gt/2005/9-3/gt-v9-n3-p08-s.pdf', 'source': {'id': 'https://openalex.org/S50220091', 'display_name': 'Geometry & Topology', 'issn_l': '1364-0380', 'issn': ['1364-0380', '1465-3060'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [{'display_name': 'Sustainable cities and communities', 'id': 'https://metadata.un.org/sdg/11', 'score': 0.72}], 'grants': [], 'datasets': [], 'versions': ['https://openalex.org/W4297571775'], 'referenced_works_count': 45, 'referenced_works': ['https://openalex.org/W1520357511', 'https://openalex.org/W1548977175', 'https://openalex.org/W1875130599', 'https://openalex.org/W1966035897', 'https://openalex.org/W1972518163', 'https://openalex.org/W1974399665', 'https://openalex.org/W1975757718', 'https://openalex.org/W1985777652', 'https://openalex.org/W1987099864', 'https://openalex.org/W1992939536', 'https://openalex.org/W1994127322', 'https://openalex.org/W1994182238', 'https://openalex.org/W1997353105', 'https://openalex.org/W2022673062', 'https://openalex.org/W2035001592', 'https://openalex.org/W2037070544', 'https://openalex.org/W2053265348', 'https://openalex.org/W2053583322', 'https://openalex.org/W2053866861', 'https://openalex.org/W2058824160', 'https://openalex.org/W2068638265', 'https://openalex.org/W2072308652', 'https://openalex.org/W2072800909', 'https://openalex.org/W2093052015', 'https://openalex.org/W2097122815', 'https://openalex.org/W2133469881', 'https://openalex.org/W2134086356', 'https://openalex.org/W2134309556', 'https://openalex.org/W2142791911', 'https://openalex.org/W2152615135', 'https://openalex.org/W2170795738', 'https://openalex.org/W2503148187', 'https://openalex.org/W2951756907', 'https://openalex.org/W2952296822', 'https://openalex.org/W2963196760', 'https://openalex.org/W2969829044', 'https://openalex.org/W3102389692', 'https://openalex.org/W4213195349', 'https://openalex.org/W4213285485', 'https://openalex.org/W4230258623', 'https://openalex.org/W4235484205', 'https://openalex.org/W4243447629', 'https://openalex.org/W4246690489', 'https://openalex.org/W626346765', 'https://openalex.org/W635079652'], 'related_works': ['https://openalex.org/W4379802100', 'https://openalex.org/W4301478900', 'https://openalex.org/W4235906205', 'https://openalex.org/W4225383385', 'https://openalex.org/W2798549588', 'https://openalex.org/W2368353738', 'https://openalex.org/W2059349845', 'https://openalex.org/W2012563259', 'https://openalex.org/W2003435949', 'https://openalex.org/W150156129'], 'abstract_inverted_index': {'We': [0, 26, 45], 'explore': [1], 'the': [2, 29, 33, 39, 58, 122, 134], 'geometry': [3], 'of': [4, 32, 38, 71, 104, 121, 124], 'nonpositively': [5], 'curved': [6], 'spaces': [7, 72], 'with': [8, 73, 79, 116], 'isolated': [9, 74, 91, 105, 135], 'flats,': [10], 'and': [11, 21, 56, 94, 107], 'its': [12, 97], 'consequences': [13], 'for': [14], 'groups': [15], 'that': [16, 28, 48, 86], 'act': [17], 'properly': [18], 'discontinuously,': [19], 'cocompactly,': [20], 'isometrically': [22], 'on': [23], 'such': [24, 50], 'spaces.': [25], 'prove': [27, 47], 'geometric': [30], 'boundary': [31, 99], 'space': [34, 89], 'is': [35, 52, 68, 100], 'an': [36, 112], 'invariant': [37], 'group': [40, 51], 'up': [41], 'to': [42, 81, 127, 140], 'equivariant': [43], 'homeomorphism.': [44], 'also': [46], 'any': [49], 'relatively': [53, 77], 'hyperbolic,': [54], 'biautomatic,': [55], 'satisfies': [57], 'Tits': [59, 98], 'Alternative.': [60], 'The': [61], 'main': [62], 'step': [63], 'in': [64, 132], 'establishing': [65], 'these': [66], 'results': [67, 123], 'a': [69, 87, 101, 128], 'characterization': [70], 'flats': [75, 92], 'as': [76], 'hyperbolic': [78], 'respect': [80], 'flats.': [82, 142], 'Finally': [83], 'we': [84, 118], 'show': [85], 'CAT(0)': [88], 'has': [90], 'if': [93, 96], 'only': [95], 'disjoint': [102], 'union': [103], 'points': [106], 'standard': [108], 'Euclidean': [109], 'spheres.': [110], 'In': [111], 'appendix': [113], 'written': [114], 'jointly': [115], 'Hindawi,': [117], 'extend': [119], 'many': [120], 'this': [125], 'article': [126], 'more': [129], 'general': [130], 'setting': [131], 'which': [133], 'subspaces': [136], 'are': [137], 'not': [138], 'required': [139], 'be': [141]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4297571775', 'counts_by_year': [{'year': 2024, 'cited_by_count': 3}, {'year': 2023, 'cited_by_count': 3}, {'year': 2022, 'cited_by_count': 2}, {'year': 2021, 'cited_by_count': 5}, {'year': 2020, 'cited_by_count': 4}, {'year': 2019, 'cited_by_count': 3}, {'year': 2018, 'cited_by_count': 1}, {'year': 2016, 'cited_by_count': 3}, {'year': 2015, 'cited_by_count': 3}, {'year': 2014, 'cited_by_count': 7}, {'year': 2013, 'cited_by_count': 3}], 'updated_date': '2024-12-08T20:00:38.515645', 'created_date': '2022-09-29'}