Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W4309433135', 'doi': 'https://doi.org/10.48550/arxiv.2004.00271', 'title': 'The fundamental group of quotients of products of some topological spaces by a finite group -- A generalization of a Theorem of Bauer-Catanese-Grunewald-Pignatelli', 'display_name': 'The fundamental group of quotients of products of some topological spaces by a finite group -- A generalization of a Theorem of Bauer-Catanese-Grunewald-Pignatelli', 'publication_year': 2020, 'publication_date': '2020-01-01', 'ids': {'openalex': 'https://openalex.org/W4309433135', 'doi': 'https://doi.org/10.48550/arxiv.2004.00271'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/2004.00271', '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': None, 'is_accepted': False, 'is_published': False}, 'type': 'preprint', 'type_crossref': 'journal-article', 'indexed_in': ['arxiv', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/abs/2004.00271', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5019928241', 'display_name': 'Rodolfo Aguilar Aguilar', 'orcid': 'https://orcid.org/0000-0003-4557-6559'}, 'institutions': [], 'countries': [], 'is_corresponding': True, 'raw_author_name': 'Aguilar, Rodolfo', 'raw_affiliation_strings': ['IF'], 'affiliations': [{'raw_affiliation_string': 'IF', 'institution_ids': []}]}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': ['https://openalex.org/A5019928241'], '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': 61}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11673', 'display_name': 'Deformations and Structures of Hom-Lie Algebras', 'score': 0.9872, 'subfield': {'id': 'https://openalex.org/subfields/2602', 'display_name': 'Algebra and Number Theory'}, '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/T11673', 'display_name': 'Deformations and Structures of Hom-Lie Algebras', 'score': 0.9872, 'subfield': {'id': 'https://openalex.org/subfields/2602', 'display_name': 'Algebra and Number Theory'}, '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/T11703', 'display_name': 'Study of properties and structures of commutative rings', 'score': 0.9844, 'subfield': {'id': 'https://openalex.org/subfields/2602', 'display_name': 'Algebra and Number Theory'}, '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/T11151', 'display_name': 'Model Theory and Topological Dynamics', 'score': 0.9833, '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/fundamental-group', 'display_name': 'Fundamental group', 'score': 0.66093445}, {'id': 'https://openalex.org/keywords/covering-space', 'display_name': 'Covering space', 'score': 0.6093691}, {'id': 'https://openalex.org/keywords/homogeneous-structures', 'display_name': 'Homogeneous Structures', 'score': 0.462406}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.79351926}, {'id': 'https://openalex.org/C199422724', 'wikidata': 'https://www.wikidata.org/wiki/Q41118', 'display_name': 'Quotient', 'level': 2, 'score': 0.6992676}, {'id': 'https://openalex.org/C159876591', 'wikidata': 'https://www.wikidata.org/wiki/Q662830', 'display_name': 'Fundamental group', 'level': 2, 'score': 0.66093445}, {'id': 'https://openalex.org/C96386209', 'wikidata': 'https://www.wikidata.org/wiki/Q1046291', 'display_name': 'Topological group', 'level': 3, 'score': 0.6579854}, {'id': 'https://openalex.org/C2781311116', 'wikidata': 'https://www.wikidata.org/wiki/Q83306', 'display_name': 'Group (periodic table)', 'level': 2, 'score': 0.6159006}, {'id': 'https://openalex.org/C162329640', 'wikidata': 'https://www.wikidata.org/wiki/Q332648', 'display_name': 'Covering space', 'level': 2, 'score': 0.6093691}, {'id': 'https://openalex.org/C2780428219', 'wikidata': 'https://www.wikidata.org/wiki/Q16952335', 'display_name': 'Cover (algebra)', 'level': 2, 'score': 0.53169596}, {'id': 'https://openalex.org/C177148314', 'wikidata': 'https://www.wikidata.org/wiki/Q170084', 'display_name': 'Generalization', 'level': 2, 'score': 0.5189559}, {'id': 'https://openalex.org/C2777404646', 'wikidata': 'https://www.wikidata.org/wiki/Q1057968', 'display_name': 'Finite group', 'level': 3, 'score': 0.47129408}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.46323556}, {'id': 'https://openalex.org/C90673727', 'wikidata': 'https://www.wikidata.org/wiki/Q901718', 'display_name': 'Product (mathematics)', 'level': 2, 'score': 0.4240868}, {'id': 'https://openalex.org/C184720557', 'wikidata': 'https://www.wikidata.org/wiki/Q7825049', 'display_name': 'Topology (electrical circuits)', 'level': 2, 'score': 0.32940376}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.29403484}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.17387402}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.13278037}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.07866487}, {'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/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C127413603', 'wikidata': 'https://www.wikidata.org/wiki/Q11023', 'display_name': 'Engineering', 'level': 0, 'score': 0.0}], 'mesh': [], 'locations_count': 9, 'locations': [{'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/2004.00271', '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': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/2004.00271', 'pdf_url': 'http://arxiv.org/pdf/2004.00271', '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://hal.archives-ouvertes.fr/hal-02525803v3/file/epiga_vol5-Aguilar-Aguilar.pdf', 'pdf_url': 'https://hal.archives-ouvertes.fr/hal-02525803v3/file/epiga_vol5-Aguilar-Aguilar.pdf', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': 'cc-by-sa', 'license_id': 'https://openalex.org/licenses/cc-by-sa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hal.science/hal-02525803v3/document', 'pdf_url': 'https://hal.science/hal-02525803v3/document', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': 'cc-by-sa', 'license_id': 'https://openalex.org/licenses/cc-by-sa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hal.archives-ouvertes.fr/hal-02525803', 'pdf_url': 'https://hal.archives-ouvertes.fr/hal-02525803/document', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': 'cc-by-sa', 'license_id': 'https://openalex.org/licenses/cc-by-sa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hal.science/hal-02525803v3/file/epiga_vol5-Aguilar-Aguilar.pdf', 'pdf_url': 'https://hal.science/hal-02525803v3/file/epiga_vol5-Aguilar-Aguilar.pdf', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': 'cc-by-sa', 'license_id': 'https://openalex.org/licenses/cc-by-sa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hal.science/hal-02525803', 'pdf_url': 'https://hal.science/hal-02525803/document', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': 'cc-by-sa', 'license_id': 'https://openalex.org/licenses/cc-by-sa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hal.archives-ouvertes.fr/hal-02525803v2/file/Fundamental%20group%20of%20product%20of%20open%20surfaces.pdf', 'pdf_url': 'https://hal.archives-ouvertes.fr/hal-02525803v2/file/Fundamental%20group%20of%20product%20of%20open%20surfaces.pdf', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], '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.2004.00271', '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/2004.00271', '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': None, 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W4309433135', 'https://openalex.org/W4300834406', 'https://openalex.org/W4287814120', 'https://openalex.org/W3105313525', 'https://openalex.org/W3014104908', 'https://openalex.org/W2758220948', 'https://openalex.org/W2725922850', 'https://openalex.org/W2165991287', 'https://openalex.org/W2078049079', 'https://openalex.org/W1598765221'], 'abstract_inverted_index': {'We': [0], 'provide': [1], 'a': [2, 12, 20, 24, 33], 'description': [3], 'of': [4, 8, 11, 14, 36, 49], 'the': [5, 9], 'fundamental': [6], 'group': [7, 26], 'quotient': [10], 'product': [13], 'topological': [15], 'spaces': [16], '$X_i$,': [17], 'each': [18], 'admitting': [19], 'universal': [21], 'cover,': [22], 'by': [23], 'finite': [25, 34], '$G$,': [27], 'provided': [28], 'that': [29], 'there': [30], 'is': [31], 'only': [32], 'number': [35], 'path-connected': [37], 'components': [38], 'in': [39], '$X_i^g$': [40], 'for': [41], 'every': [42], '$g\\in': [43], 'G$.': [44], 'This': [45], 'generalizes': [46], 'previous': [47], 'work': [48], 'Bauer-Catanese-Grunewald-Pignatelli': [50], 'and': [51], 'Dedieu-Perroni.': [52]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4309433135', 'counts_by_year': [], 'updated_date': '2024-09-19T19:13:09.438238', 'created_date': '2022-11-27'}