On the Borromean arithmetic orbifolds

We revisit the fundamental groups Gmnp of the orbifolds Bmnp, where the underlying manifold is the 3-sphere S3 and the Borromean rings are the singular set with isotropies of order m, n and p. We correct an omission in [2] and show that Gmnp is arithmetic if and only if (m,n,p) is one of the 12 trip...

Full description

Saved in:
Bibliographic Details
Published in:Topology and its applications 2023-11, Vol.339, p.108576, Article 108576
Main Authors: Lozano, María Teresa, Montesinos-Amilibia, José María
Format: Article
Language:English
Subjects:
Arithmetic group
Borromean link
Knots
Orbifold
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c298t-6912c52f99984ea9e0b7be3fa4ad681280056f878b4ab08180887e01d315b7f03
container_end_page
container_issue
container_start_page 108576
container_title Topology and its applications
container_volume 339
creator Lozano, María Teresa
Montesinos-Amilibia, José María
description We revisit the fundamental groups Gmnp of the orbifolds Bmnp, where the underlying manifold is the 3-sphere S3 and the Borromean rings are the singular set with isotropies of order m, n and p. We correct an omission in [2] and show that Gmnp is arithmetic if and only if (m,n,p) is one of the 12 triples (3,3,3), (3,3,∞), (3,4,4), (3,4,∞), (3,6,6), (3,∞,∞), (4,4,4), (4,4,∞), (4,∞,∞), (6,6,6), (6,6,∞), (∞,∞,∞). The main purpose of the paper is to present each Gmnp, arithmetic, as a group of 4×4 matrices with entries in the ring of integers of a totally real number field K, and which are automorphs of a quaternary form F with entries in K of Sylvester type (+,+,+,−).
doi_str_mv 10.1016/j.topol.2023.108576
format article
fullrecord <record><control><sourceid>elsevier_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1016_j_topol_2023_108576</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0166864123001700</els_id><sourcerecordid>S0166864123001700</sourcerecordid><originalsourceid>FETCH-LOGICAL-c298t-6912c52f99984ea9e0b7be3fa4ad681280056f878b4ab08180887e01d315b7f03</originalsourceid><addsrcrecordid>eNp9jz1PwzAURS0EEqXwC1iyMKY8O4n9PDBAxZdUqQvMluM8q47SurIjJP49KWFmetLVO1f3MHbLYcWBy_t-NcZjHFYCRDUl2Ch5xhYclS4rAeqcLaYvWaKs-SW7yrkHAK6VWLC77aEYd1Q8xZTinuyhsCmMuz2NwRUxtcHHocvX7MLbIdPN312yz5fnj_Vbudm-vq8fN6UTGsdSai5cI7zWGmuymqBVLVXe1raTyAUCNNKjwra2LSBHQFQEvKt40yoP1ZJVc69LMedE3hxT2Nv0bTiYk6npza-pOZma2XSiHmaKpmlfgZLJLtDBURcSudF0MfzL_wB8y1wT</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On the Borromean arithmetic orbifolds</title><source>ScienceDirect Journals</source><creator>Lozano, María Teresa ; Montesinos-Amilibia, José María</creator><creatorcontrib>Lozano, María Teresa ; Montesinos-Amilibia, José María</creatorcontrib><description>We revisit the fundamental groups Gmnp of the orbifolds Bmnp, where the underlying manifold is the 3-sphere S3 and the Borromean rings are the singular set with isotropies of order m, n and p. We correct an omission in [2] and show that Gmnp is arithmetic if and only if (m,n,p) is one of the 12 triples (3,3,3), (3,3,∞), (3,4,4), (3,4,∞), (3,6,6), (3,∞,∞), (4,4,4), (4,4,∞), (4,∞,∞), (6,6,6), (6,6,∞), (∞,∞,∞). The main purpose of the paper is to present each Gmnp, arithmetic, as a group of 4×4 matrices with entries in the ring of integers of a totally real number field K, and which are automorphs of a quaternary form F with entries in K of Sylvester type (+,+,+,−).</description><identifier>ISSN: 0166-8641</identifier><identifier>EISSN: 1879-3207</identifier><identifier>DOI: 10.1016/j.topol.2023.108576</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Arithmetic group ; Borromean link ; Knots ; Orbifold</subject><ispartof>Topology and its applications, 2023-11, Vol.339, p.108576, Article 108576</ispartof><rights>2023 The Author(s)</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c298t-6912c52f99984ea9e0b7be3fa4ad681280056f878b4ab08180887e01d315b7f03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Lozano, María Teresa</creatorcontrib><creatorcontrib>Montesinos-Amilibia, José María</creatorcontrib><title>On the Borromean arithmetic orbifolds</title><title>Topology and its applications</title><description>We revisit the fundamental groups Gmnp of the orbifolds Bmnp, where the underlying manifold is the 3-sphere S3 and the Borromean rings are the singular set with isotropies of order m, n and p. We correct an omission in [2] and show that Gmnp is arithmetic if and only if (m,n,p) is one of the 12 triples (3,3,3), (3,3,∞), (3,4,4), (3,4,∞), (3,6,6), (3,∞,∞), (4,4,4), (4,4,∞), (4,∞,∞), (6,6,6), (6,6,∞), (∞,∞,∞). The main purpose of the paper is to present each Gmnp, arithmetic, as a group of 4×4 matrices with entries in the ring of integers of a totally real number field K, and which are automorphs of a quaternary form F with entries in K of Sylvester type (+,+,+,−).</description><subject>Arithmetic group</subject><subject>Borromean link</subject><subject>Knots</subject><subject>Orbifold</subject><issn>0166-8641</issn><issn>1879-3207</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9jz1PwzAURS0EEqXwC1iyMKY8O4n9PDBAxZdUqQvMluM8q47SurIjJP49KWFmetLVO1f3MHbLYcWBy_t-NcZjHFYCRDUl2Ch5xhYclS4rAeqcLaYvWaKs-SW7yrkHAK6VWLC77aEYd1Q8xZTinuyhsCmMuz2NwRUxtcHHocvX7MLbIdPN312yz5fnj_Vbudm-vq8fN6UTGsdSai5cI7zWGmuymqBVLVXe1raTyAUCNNKjwra2LSBHQFQEvKt40yoP1ZJVc69LMedE3hxT2Nv0bTiYk6npza-pOZma2XSiHmaKpmlfgZLJLtDBURcSudF0MfzL_wB8y1wT</recordid><startdate>20231101</startdate><enddate>20231101</enddate><creator>Lozano, María Teresa</creator><creator>Montesinos-Amilibia, José María</creator><general>Elsevier B.V</general><scope>6I.</scope><scope>AAFTH</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20231101</creationdate><title>On the Borromean arithmetic orbifolds</title><author>Lozano, María Teresa ; Montesinos-Amilibia, José María</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c298t-6912c52f99984ea9e0b7be3fa4ad681280056f878b4ab08180887e01d315b7f03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Arithmetic group</topic><topic>Borromean link</topic><topic>Knots</topic><topic>Orbifold</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lozano, María Teresa</creatorcontrib><creatorcontrib>Montesinos-Amilibia, José María</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>CrossRef</collection><jtitle>Topology and its applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lozano, María Teresa</au><au>Montesinos-Amilibia, José María</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Borromean arithmetic orbifolds</atitle><jtitle>Topology and its applications</jtitle><date>2023-11-01</date><risdate>2023</risdate><volume>339</volume><spage>108576</spage><pages>108576-</pages><artnum>108576</artnum><issn>0166-8641</issn><eissn>1879-3207</eissn><abstract>We revisit the fundamental groups Gmnp of the orbifolds Bmnp, where the underlying manifold is the 3-sphere S3 and the Borromean rings are the singular set with isotropies of order m, n and p. We correct an omission in [2] and show that Gmnp is arithmetic if and only if (m,n,p) is one of the 12 triples (3,3,3), (3,3,∞), (3,4,4), (3,4,∞), (3,6,6), (3,∞,∞), (4,4,4), (4,4,∞), (4,∞,∞), (6,6,6), (6,6,∞), (∞,∞,∞). The main purpose of the paper is to present each Gmnp, arithmetic, as a group of 4×4 matrices with entries in the ring of integers of a totally real number field K, and which are automorphs of a quaternary form F with entries in K of Sylvester type (+,+,+,−).</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.topol.2023.108576</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0166-8641
ispartof Topology and its applications, 2023-11, Vol.339, p.108576, Article 108576
issn 0166-8641
1879-3207
language eng
recordid cdi_crossref_primary_10_1016_j_topol_2023_108576
source ScienceDirect Journals
subjects Arithmetic group
Borromean link
Knots
Orbifold
title On the Borromean arithmetic orbifolds
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T02%3A54%3A30IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-elsevier_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20Borromean%20arithmetic%20orbifolds&rft.jtitle=Topology%20and%20its%20applications&rft.au=Lozano,%20Mar%C3%ADa%20Teresa&rft.date=2023-11-01&rft.volume=339&rft.spage=108576&rft.pages=108576-&rft.artnum=108576&rft.issn=0166-8641&rft.eissn=1879-3207&rft_id=info:doi/10.1016/j.topol.2023.108576&rft_dat=%3Celsevier_cross%3ES0166864123001700%3C/elsevier_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c298t-6912c52f99984ea9e0b7be3fa4ad681280056f878b4ab08180887e01d315b7f03%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true