A construction of hyperbolic Coxeter groups

Name: Work Video:
Duration: 3 min 30 s
Description: We give a simple construction of Gromov hyperbolic Coxeter groups of arbitrarily large virtual cohomological dimension. Our construction provides new examples of such groups. Using this one can construct, e.g., new groups having some interesting asphericity properties.
Damian Osajda
{'id': 'https://openalex.org/W2963192238', 'doi': 'https://doi.org/10.4171/cmh/288', 'title': 'A construction of hyperbolic Coxeter groups', 'display_name': 'A construction of hyperbolic Coxeter groups', 'publication_year': 2013, 'publication_date': '2013-04-24', 'ids': {'openalex': 'https://openalex.org/W2963192238', 'doi': 'https://doi.org/10.4171/cmh/288', 'mag': '2963192238'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.4171/cmh/288', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S175700853', 'display_name': 'Commentarii Mathematici Helvetici', 'issn_l': '0010-2571', 'issn': ['0010-2571', '1420-8946'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4310316982', 'host_organization_name': 'European Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310316982'], 'host_organization_lineage_names': ['European Mathematical Society'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'https://doi.org/10.4171/cmh/288', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5028539166', 'display_name': 'Damian Osajda', 'orcid': 'https://orcid.org/0000-0002-5412-8443'}, 'institutions': [{'id': 'https://openalex.org/I219388962', 'display_name': 'University of Wrocław', 'ror': 'https://ror.org/00yae6e25', 'country_code': 'PL', 'type': 'education', 'lineage': ['https://openalex.org/I219388962']}], 'countries': ['PL'], 'is_corresponding': True, 'raw_author_name': 'Damian Osajda', 'raw_affiliation_strings': ['Uniwersytet Wrocławski, Poland'], 'affiliations': [{'raw_affiliation_string': 'Uniwersytet Wrocławski, Poland', 'institution_ids': ['https://openalex.org/I219388962']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': ['https://openalex.org/A5028539166'], 'corresponding_institution_ids': ['https://openalex.org/I219388962'], 'apc_list': {'value': 0, 'currency': 'USD', 'value_usd': 0, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 1.977, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 28, 'citation_normalized_percentile': {'value': 0.916885, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 92, 'max': 93}, 'biblio': {'volume': '88', 'issue': '2', 'first_page': '353', 'last_page': '367'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10304', 'display_name': 'Geometric and Algebraic Topology', '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/T10304', 'display_name': 'Geometric and Algebraic Topology', '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/T10948', 'display_name': 'Advanced Combinatorial Mathematics', 'score': 0.9996, '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/T10896', 'display_name': 'Homotopy and Cohomology in Algebraic Topology', 'score': 0.998, '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/cohomological-dimension', 'display_name': 'Cohomological dimension', 'score': 0.710711}], 'concepts': [{'id': 'https://openalex.org/C143669375', 'wikidata': 'https://www.wikidata.org/wiki/Q7874246', 'display_name': 'Coxeter group', 'level': 2, 'score': 0.98644125}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.87198734}, {'id': 'https://openalex.org/C2778332477', 'wikidata': 'https://www.wikidata.org/wiki/Q5141396', 'display_name': 'Cohomological dimension', 'level': 3, 'score': 0.710711}, {'id': 'https://openalex.org/C37486056', 'wikidata': 'https://www.wikidata.org/wiki/Q5179939', 'display_name': 'Coxeter complex', 'level': 4, 'score': 0.70232034}, {'id': 'https://openalex.org/C33676613', 'wikidata': 'https://www.wikidata.org/wiki/Q13415176', 'display_name': 'Dimension (graph theory)', 'level': 2, 'score': 0.6094558}, {'id': 'https://openalex.org/C57796230', 'wikidata': 'https://www.wikidata.org/wiki/Q899720', 'display_name': 'Point group', 'level': 2, 'score': 0.57039815}, {'id': 'https://openalex.org/C201064014', 'wikidata': 'https://www.wikidata.org/wiki/Q3956993', 'display_name': 'Artin group', 'level': 3, 'score': 0.56516117}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.51811284}, {'id': 'https://openalex.org/C2780801425', 'wikidata': 'https://www.wikidata.org/wiki/Q5164392', 'display_name': 'Construct (python library)', 'level': 2, 'score': 0.50778943}, {'id': 'https://openalex.org/C2780586882', 'wikidata': 'https://www.wikidata.org/wiki/Q7520643', 'display_name': 'Simple (philosophy)', 'level': 2, 'score': 0.43411803}, {'id': 'https://openalex.org/C2781311116', 'wikidata': 'https://www.wikidata.org/wiki/Q83306', 'display_name': 'Group (periodic table)', 'level': 2, 'score': 0.4120948}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.33782345}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.32787108}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.07578859}, {'id': 'https://openalex.org/C78606066', 'wikidata': 'https://www.wikidata.org/wiki/Q1198376', 'display_name': 'Cohomology', 'level': 2, 'score': 0.04013872}, {'id': 'https://openalex.org/C199360897', 'wikidata': 'https://www.wikidata.org/wiki/Q9143', 'display_name': 'Programming language', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C178790620', 'wikidata': 'https://www.wikidata.org/wiki/Q11351', 'display_name': 'Organic chemistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C138885662', 'wikidata': 'https://www.wikidata.org/wiki/Q5891', 'display_name': 'Philosophy', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C111472728', 'wikidata': 'https://www.wikidata.org/wiki/Q9471', 'display_name': 'Epistemology', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 4, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.4171/cmh/288', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S175700853', 'display_name': 'Commentarii Mathematici Helvetici', 'issn_l': '0010-2571', 'issn': ['0010-2571', '1420-8946'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4310316982', 'host_organization_name': 'European Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310316982'], 'host_organization_lineage_names': ['European Mathematical Society'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1003.0774', 'pdf_url': 'https://arxiv.org/pdf/1003.0774', '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': 'http://arxiv.org/abs/1003.0774', 'pdf_url': 'http://arxiv.org/pdf/1003.0774', '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': 'http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.726.326', 'pdf_url': 'http://www.math.uni.wroc.pl/%7Edosaj/trav/chcg-web.pdf', 'source': {'id': 'https://openalex.org/S4306400349', 'display_name': 'CiteSeer X (The Pennsylvania State University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I130769515', 'host_organization_name': 'Pennsylvania State University', 'host_organization_lineage': ['https://openalex.org/I130769515'], 'host_organization_lineage_names': ['Pennsylvania State University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.4171/cmh/288', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S175700853', 'display_name': 'Commentarii Mathematici Helvetici', 'issn_l': '0010-2571', 'issn': ['0010-2571', '1420-8946'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4310316982', 'host_organization_name': 'European Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310316982'], 'host_organization_lineage_names': ['European Mathematical Society'], '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': 0.77}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 16, 'referenced_works': ['https://openalex.org/W145940276', 'https://openalex.org/W1520357511', 'https://openalex.org/W1526820527', 'https://openalex.org/W1799638912', 'https://openalex.org/W1988589845', 'https://openalex.org/W2005692736', 'https://openalex.org/W2077194160', 'https://openalex.org/W2102407552', 'https://openalex.org/W2120504215', 'https://openalex.org/W2131329426', 'https://openalex.org/W2159139205', 'https://openalex.org/W3101919170', 'https://openalex.org/W4236305466', 'https://openalex.org/W635079652', 'https://openalex.org/W66887941', 'https://openalex.org/W749223900'], 'related_works': ['https://openalex.org/W3129492217', 'https://openalex.org/W2991273408', 'https://openalex.org/W2989843050', 'https://openalex.org/W2973247669', 'https://openalex.org/W2963192238', 'https://openalex.org/W2898698596', 'https://openalex.org/W2120504215', 'https://openalex.org/W2087186172', 'https://openalex.org/W1985041334', 'https://openalex.org/W1674264548'], 'abstract_inverted_index': {'We': [0], 'give': [1], 'a': [2], 'simple': [3], 'construction': [4, 17], 'of': [5, 10, 21], 'Gromov': [6], 'hyperbolic': [7], 'Coxeter': [8], 'groups': [9, 31], 'arbitrarily': [11], 'large': [12], 'virtual': [13], 'cohomological': [14], 'dimension.': [15], 'Our': [16], 'provides': [18], 'new': [19, 30], 'examples': [20], 'such': [22], 'groups.': [23], 'Using': [24], 'this': [25], 'one': [26], 'can': [27], 'construct,': [28], 'e.g.,': [29], 'having': [32], 'some': [33], 'interesting': [34], 'asphericity': [35], 'properties.': [36]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2963192238', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2022, 'cited_by_count': 1}, {'year': 2021, 'cited_by_count': 3}, {'year': 2020, 'cited_by_count': 6}, {'year': 2019, 'cited_by_count': 4}, {'year': 2018, 'cited_by_count': 2}, {'year': 2017, 'cited_by_count': 2}, {'year': 2015, 'cited_by_count': 6}, {'year': 2014, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 1}], 'updated_date': '2024-12-26T13:22:45.560238', 'created_date': '2019-07-30'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
