On Cantor Sets in 3‐Manifolds and Branched Coverings

It is known that any Cantor set C in a 3‐manifold M (open or closed) is tamely embedded in the boundary of a k‐cell Δ, for k = 2, 3 (R. P. Osborne, 1969). It is proved that there exist a k‐cell Δ and a 3‐fold branched covering of M over (a subset of) S3 such that (i) C is tamely embedded in the boun...

Full description

Saved in:
Bibliographic Details
Published in:Quarterly journal of mathematics 2003-06, Vol.54 (2), p.209-212
Main Author: Montesinos-Amilibia, J. M.
Format: Article
Language:English
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page 212
container_issue 2
container_start_page 209
container_title Quarterly journal of mathematics
container_volume 54
creator Montesinos-Amilibia, J. M.
description It is known that any Cantor set C in a 3‐manifold M (open or closed) is tamely embedded in the boundary of a k‐cell Δ, for k = 2, 3 (R. P. Osborne, 1969). It is proved that there exist a k‐cell Δ and a 3‐fold branched covering of M over (a subset of) S3 such that (i) C is tamely embedded in the boundary of Δ, (ii) Δ projects homeomorphically onto a k‐cell Δ̂ tamely embedded in S3, and (iii) C is sent onto a tame Cantor set T tamely embedded in the boundary of Δ̂. The argument uses techniques of branched coverings and is independent of Osborne's theorem.
doi_str_mv 10.1093/qmath/hag007
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_229839560</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>520494601</sourcerecordid><originalsourceid>FETCH-LOGICAL-c255t-1b4799cd967760350d3a376b92715246ca560238880bbb2c12c245ead2796eb23</originalsourceid><addsrcrecordid>eNo9kEtOwzAURS0EEqUwYwEWY0L9_wwhAkrVqkiAhJhYjuO2Ka1T7BTBjCWwRlZCIIjRm5x379UB4BijM4w0HbysbbMYLOwcIbkDepgJllHF5C7oIURpxgUS--AgpSVCWDAle0BMA8xtaOoI73yTYBUg_fr4nNhQzepVmaANJbyINriFL2Fev_pYhXk6BHszu0r-6O_2wcPV5X0-zMbT65v8fJw5wnmT4YJJrV2phZQCUY5KaqkUhSYSc8KEs-0kQpVSqCgK4jBxhHFvSyK18AWhfXDS5W5i_bL1qTHLehtDW2kI0Yrq9r-FTjvIxTql6GdmE6u1je8GI_MjxvyKMZ2YFs86vEqNf_tnbXw2QlLJzfDxyajbiR4NMTMj-g1dA2UH</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>229839560</pqid></control><display><type>article</type><title>On Cantor Sets in 3‐Manifolds and Branched Coverings</title><source>Oxford Journals Online</source><creator>Montesinos-Amilibia, J. M.</creator><creatorcontrib>Montesinos-Amilibia, J. M.</creatorcontrib><description>It is known that any Cantor set C in a 3‐manifold M (open or closed) is tamely embedded in the boundary of a k‐cell Δ, for k = 2, 3 (R. P. Osborne, 1969). It is proved that there exist a k‐cell Δ and a 3‐fold branched covering of M over (a subset of) S3 such that (i) C is tamely embedded in the boundary of Δ, (ii) Δ projects homeomorphically onto a k‐cell Δ̂ tamely embedded in S3, and (iii) C is sent onto a tame Cantor set T tamely embedded in the boundary of Δ̂. The argument uses techniques of branched coverings and is independent of Osborne's theorem.</description><identifier>ISSN: 0033-5606</identifier><identifier>EISSN: 1464-3847</identifier><identifier>DOI: 10.1093/qmath/hag007</identifier><language>eng</language><publisher>Oxford: Oxford University Press</publisher><ispartof>Quarterly journal of mathematics, 2003-06, Vol.54 (2), p.209-212</ispartof><rights>Copyright Oxford University Press(England) Jun 2003</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Montesinos-Amilibia, J. M.</creatorcontrib><title>On Cantor Sets in 3‐Manifolds and Branched Coverings</title><title>Quarterly journal of mathematics</title><addtitle>Q J Math</addtitle><description>It is known that any Cantor set C in a 3‐manifold M (open or closed) is tamely embedded in the boundary of a k‐cell Δ, for k = 2, 3 (R. P. Osborne, 1969). It is proved that there exist a k‐cell Δ and a 3‐fold branched covering of M over (a subset of) S3 such that (i) C is tamely embedded in the boundary of Δ, (ii) Δ projects homeomorphically onto a k‐cell Δ̂ tamely embedded in S3, and (iii) C is sent onto a tame Cantor set T tamely embedded in the boundary of Δ̂. The argument uses techniques of branched coverings and is independent of Osborne's theorem.</description><issn>0033-5606</issn><issn>1464-3847</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2003</creationdate><recordtype>article</recordtype><recordid>eNo9kEtOwzAURS0EEqUwYwEWY0L9_wwhAkrVqkiAhJhYjuO2Ka1T7BTBjCWwRlZCIIjRm5x379UB4BijM4w0HbysbbMYLOwcIbkDepgJllHF5C7oIURpxgUS--AgpSVCWDAle0BMA8xtaOoI73yTYBUg_fr4nNhQzepVmaANJbyINriFL2Fev_pYhXk6BHszu0r-6O_2wcPV5X0-zMbT65v8fJw5wnmT4YJJrV2phZQCUY5KaqkUhSYSc8KEs-0kQpVSqCgK4jBxhHFvSyK18AWhfXDS5W5i_bL1qTHLehtDW2kI0Yrq9r-FTjvIxTql6GdmE6u1je8GI_MjxvyKMZ2YFs86vEqNf_tnbXw2QlLJzfDxyajbiR4NMTMj-g1dA2UH</recordid><startdate>200306</startdate><enddate>200306</enddate><creator>Montesinos-Amilibia, J. M.</creator><general>Oxford University Press</general><general>Oxford Publishing Limited (England)</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>200306</creationdate><title>On Cantor Sets in 3‐Manifolds and Branched Coverings</title><author>Montesinos-Amilibia, J. M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c255t-1b4799cd967760350d3a376b92715246ca560238880bbb2c12c245ead2796eb23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2003</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Montesinos-Amilibia, J. M.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Quarterly journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Montesinos-Amilibia, J. M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Cantor Sets in 3‐Manifolds and Branched Coverings</atitle><jtitle>Quarterly journal of mathematics</jtitle><addtitle>Q J Math</addtitle><date>2003-06</date><risdate>2003</risdate><volume>54</volume><issue>2</issue><spage>209</spage><epage>212</epage><pages>209-212</pages><issn>0033-5606</issn><eissn>1464-3847</eissn><abstract>It is known that any Cantor set C in a 3‐manifold M (open or closed) is tamely embedded in the boundary of a k‐cell Δ, for k = 2, 3 (R. P. Osborne, 1969). It is proved that there exist a k‐cell Δ and a 3‐fold branched covering of M over (a subset of) S3 such that (i) C is tamely embedded in the boundary of Δ, (ii) Δ projects homeomorphically onto a k‐cell Δ̂ tamely embedded in S3, and (iii) C is sent onto a tame Cantor set T tamely embedded in the boundary of Δ̂. The argument uses techniques of branched coverings and is independent of Osborne's theorem.</abstract><cop>Oxford</cop><pub>Oxford University Press</pub><doi>10.1093/qmath/hag007</doi><tpages>4</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0033-5606
ispartof Quarterly journal of mathematics, 2003-06, Vol.54 (2), p.209-212
issn 0033-5606
1464-3847
language eng
recordid cdi_proquest_journals_229839560
source Oxford Journals Online
title On Cantor Sets in 3‐Manifolds and Branched Coverings
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-08T09%3A09%3A25IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20Cantor%20Sets%20in%203%E2%80%90Manifolds%20and%20Branched%20Coverings&rft.jtitle=Quarterly%20journal%20of%20mathematics&rft.au=Montesinos-Amilibia,%20J.%20M.&rft.date=2003-06&rft.volume=54&rft.issue=2&rft.spage=209&rft.epage=212&rft.pages=209-212&rft.issn=0033-5606&rft.eissn=1464-3847&rft_id=info:doi/10.1093/qmath/hag007&rft_dat=%3Cproquest_cross%3E520494601%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c255t-1b4799cd967760350d3a376b92715246ca560238880bbb2c12c245ead2796eb23%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=229839560&rft_id=info:pmid/&rfr_iscdi=true