{"id":{"repo_id":"soton","oai_identifier":"oai:eprints.soton.ac.uk:50613"},"canonical_url":"https://search.dev.ndltd.org/etd/soton/oai:eprints.soton.ac.uk:50613","repository":{"repo_id":"soton","name":"University of Southampton","base_url":"https://eprints.soton.ac.uk/cgi/oai2"},"display":{"title":"The CAT(0) dimension of 3-generator Artin groups","abstract":"The three generator Artin groups A(m,n.2) are known to be have CAT(O) dimension strictly greater than two if both m and n are odd [BC]. In Chapter 1 we introduce the notions of CAT(O) dimension and three generator Artin<br/>groups.<br/><br/>In Chapter 2 we show that if one of m or n is even, then the three generator Artin group has CAT(O) dimension two.<br/><br/>In Chapter 3 we extend work by Noel Brady and John Crisp [BC] to enlarge the subclass of groups A(m.n.2) known to have CAT(O) dimension three.<br/><br/>In Chapter 4 we classify the structure of a canonical cell complex which the group A(m,n,2) acts on for the case where m is even, greater or equal to six and not divisible by four and n is prime, greater or equal to five.<br/><br/>Finally, in Chapter 5 we use the results of Chapter 4 to exhibit classes of rank four Artin groups with CAT(O) dimension two. and a class of rank six Artin groups with CAT(O) dimension two.","abstract_html":"The three generator Artin groups A(m,n.2) are known to be have CAT(O) dimension strictly greater than two if both m and n are odd [BC]. In Chapter 1 we introduce the notions of CAT(O) dimension and three generator Artin&lt;br/&gt;groups.&lt;br/&gt;&lt;br/&gt;In Chapter 2 we show that if one of m or n is even, then the three generator Artin group has CAT(O) dimension two.&lt;br/&gt;&lt;br/&gt;In Chapter 3 we extend work by Noel Brady and John Crisp [BC] to enlarge the subclass of groups A(m.n.2) known to have CAT(O) dimension three.&lt;br/&gt;&lt;br/&gt;In Chapter 4 we classify the structure of a canonical cell complex which the group A(m,n,2) acts on for the case where m is even, greater or equal to six and not divisible by four and n is prime, greater or equal to five.&lt;br/&gt;&lt;br/&gt;Finally, in Chapter 5 we use the results of Chapter 4 to exhibit classes of rank four Artin groups with CAT(O) dimension two. and a class of rank six Artin groups with CAT(O) dimension two.","abstract_has_math":false,"creators":["Hanham, Paul Edward"],"institution":"University of Southampton","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Niblo, Graham"],"committee_chairs":[],"committee_members":[],"year":2002,"date_issued":"2002-10","date_published":"2002-10","updated_at":"2026-07-24T04:35:50Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Niblo, Graham"]},{"key":"dc:creator","label":"Author","values":["Hanham, Paul Edward"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2002-10"]},{"key":"dc:date.issued","label":"Date","values":["2002-10"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Mathematics (pre 2011 reorg)","Faculty of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Southampton"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://eprints.soton.ac.uk/50613/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Ph.D."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://eprints.soton.ac.uk/50613/1/00247959.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The three generator Artin groups A(m,n.2) are known to be have CAT(O) dimension strictly greater than two if both m and n are odd [BC]. In Chapter 1 we introduce the notions of CAT(O) dimension and three generator Artin<br/>groups.<br/><br/>In Chapter 2 we show that if one of m or n is even, then the three generator Artin group has CAT(O) dimension two.<br/><br/>In Chapter 3 we extend work by Noel Brady and John Crisp [BC] to enlarge the subclass of groups A(m.n.2) known to have CAT(O) dimension three.<br/><br/>In Chapter 4 we classify the structure of a canonical cell complex which the group A(m,n,2) acts on for the case where m is even, greater or equal to six and not divisible by four and n is prime, greater or equal to five.<br/><br/>Finally, in Chapter 5 we use the results of Chapter 4 to exhibit classes of rank four Artin groups with CAT(O) dimension two. and a class of rank six Artin groups with CAT(O) dimension two."]},{"key":"dc:format","label":"Dc Format","values":["text"]},{"key":"dc:title","label":"Title","values":["The CAT(0) dimension of 3-generator Artin groups"]}]}],"canonical_facts":{"dc:contributor.advisor":["Niblo, Graham"],"dc:creator":["Hanham, Paul Edward"],"dc:date":["2002-10"],"dc:date.issued":["2002-10"],"dc:description.abstract":["The three generator Artin groups A(m,n.2) are known to be have CAT(O) dimension strictly greater than two if both m and n are odd [BC]. In Chapter 1 we introduce the notions of CAT(O) dimension and three generator Artin<br/>groups.<br/><br/>In Chapter 2 we show that if one of m or n is even, then the three generator Artin group has CAT(O) dimension two.<br/><br/>In Chapter 3 we extend work by Noel Brady and John Crisp [BC] to enlarge the subclass of groups A(m.n.2) known to have CAT(O) dimension three.<br/><br/>In Chapter 4 we classify the structure of a canonical cell complex which the group A(m,n,2) acts on for the case where m is even, greater or equal to six and not divisible by four and n is prime, greater or equal to five.<br/><br/>Finally, in Chapter 5 we use the results of Chapter 4 to exhibit classes of rank four Artin groups with CAT(O) dimension two. and a class of rank six Artin groups with CAT(O) dimension two."],"dc:format":["text"],"dc:identifier.uri":["https://eprints.soton.ac.uk/50613/1/00247959.pdf"],"dc:publisher.department":["Mathematics (pre 2011 reorg)","Faculty of Mathematics"],"dc:publisher.institution":["University of Southampton"],"dc:relation.isreferencedby":["https://eprints.soton.ac.uk/50613/"],"dc:title":["The CAT(0) dimension of 3-generator Artin groups"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["Ph.D."]},"updated_at":"2026-07-24T04:35:50Z"}