The 0-concordance monoid admits an infinite linearly independent set

Under the relation of \(0\)-concordance, the set of knotted 2-spheres in \(S^4\) forms a commutative monoid \(\mathcal{M}_0\) with the operation of connected sum. Sunukjian has recently shown that \(\mathcal{M}_0\) contains a submonoid isomorphic to \(\mathbb{Z}^{\ge 0}\). In this note, we show that...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-09
Main Authors: Dai, Irving, Miller, Maggie
Format: Article
Language:English
Subjects:
Homology
Monoids
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Dai, Irving
Miller, Maggie
description Under the relation of \(0\)-concordance, the set of knotted 2-spheres in \(S^4\) forms a commutative monoid \(\mathcal{M}_0\) with the operation of connected sum. Sunukjian has recently shown that \(\mathcal{M}_0\) contains a submonoid isomorphic to \(\mathbb{Z}^{\ge 0}\). In this note, we show that \(\mathcal{M}_0\) contains a submonoid isomorphic to \((\mathbb{Z}^{\ge 0})^\infty\). Our argument relates the \(0\)-concordance monoid to linear independence of certain Seifert solids in the (spin) rational homology cobordism group.
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2259089550</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2259089550</sourcerecordid><originalsourceid>FETCH-proquest_journals_22590895503</originalsourceid><addsrcrecordid>eNqNik0KwjAQRoMgWLR3GHBdiJNG27U_eIDuS2immNJOapIuvL1deAA334P3vo3IUKlTUZWIO5HHOEgp8XxBrVUmbs2LQBad584Ha7gjmDx7Z8HYyaUIhsFx79glgtExmTB-VmNppnU4QaR0ENvejJHyH_fi-Lg312cxB_9eKKZ28EvgNbWIupZVrbVU_72-I_k6hw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2259089550</pqid></control><display><type>article</type><title>The 0-concordance monoid admits an infinite linearly independent set</title><source>Publicly Available Content Database</source><creator>Dai, Irving ; Miller, Maggie</creator><creatorcontrib>Dai, Irving ; Miller, Maggie</creatorcontrib><description>Under the relation of \(0\)-concordance, the set of knotted 2-spheres in \(S^4\) forms a commutative monoid \(\mathcal{M}_0\) with the operation of connected sum. Sunukjian has recently shown that \(\mathcal{M}_0\) contains a submonoid isomorphic to \(\mathbb{Z}^{\ge 0}\). In this note, we show that \(\mathcal{M}_0\) contains a submonoid isomorphic to \((\mathbb{Z}^{\ge 0})^\infty\). Our argument relates the \(0\)-concordance monoid to linear independence of certain Seifert solids in the (spin) rational homology cobordism group.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Homology ; Monoids</subject><ispartof>arXiv.org, 2023-09</ispartof><rights>2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2259089550?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25753,37012,44590</link.rule.ids></links><search><creatorcontrib>Dai, Irving</creatorcontrib><creatorcontrib>Miller, Maggie</creatorcontrib><title>The 0-concordance monoid admits an infinite linearly independent set</title><title>arXiv.org</title><description>Under the relation of \(0\)-concordance, the set of knotted 2-spheres in \(S^4\) forms a commutative monoid \(\mathcal{M}_0\) with the operation of connected sum. Sunukjian has recently shown that \(\mathcal{M}_0\) contains a submonoid isomorphic to \(\mathbb{Z}^{\ge 0}\). In this note, we show that \(\mathcal{M}_0\) contains a submonoid isomorphic to \((\mathbb{Z}^{\ge 0})^\infty\). Our argument relates the \(0\)-concordance monoid to linear independence of certain Seifert solids in the (spin) rational homology cobordism group.</description><subject>Homology</subject><subject>Monoids</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNik0KwjAQRoMgWLR3GHBdiJNG27U_eIDuS2immNJOapIuvL1deAA334P3vo3IUKlTUZWIO5HHOEgp8XxBrVUmbs2LQBad584Ha7gjmDx7Z8HYyaUIhsFx79glgtExmTB-VmNppnU4QaR0ENvejJHyH_fi-Lg312cxB_9eKKZ28EvgNbWIupZVrbVU_72-I_k6hw</recordid><startdate>20230903</startdate><enddate>20230903</enddate><creator>Dai, Irving</creator><creator>Miller, Maggie</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope></search><sort><creationdate>20230903</creationdate><title>The 0-concordance monoid admits an infinite linearly independent set</title><author>Dai, Irving ; Miller, Maggie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_22590895503</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Homology</topic><topic>Monoids</topic><toplevel>online_resources</toplevel><creatorcontrib>Dai, Irving</creatorcontrib><creatorcontrib>Miller, Maggie</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dai, Irving</au><au>Miller, Maggie</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>The 0-concordance monoid admits an infinite linearly independent set</atitle><jtitle>arXiv.org</jtitle><date>2023-09-03</date><risdate>2023</risdate><eissn>2331-8422</eissn><abstract>Under the relation of \(0\)-concordance, the set of knotted 2-spheres in \(S^4\) forms a commutative monoid \(\mathcal{M}_0\) with the operation of connected sum. Sunukjian has recently shown that \(\mathcal{M}_0\) contains a submonoid isomorphic to \(\mathbb{Z}^{\ge 0}\). In this note, we show that \(\mathcal{M}_0\) contains a submonoid isomorphic to \((\mathbb{Z}^{\ge 0})^\infty\). Our argument relates the \(0\)-concordance monoid to linear independence of certain Seifert solids in the (spin) rational homology cobordism group.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2023-09
issn 2331-8422
language eng
recordid cdi_proquest_journals_2259089550
source Publicly Available Content Database
subjects Homology
Monoids
title The 0-concordance monoid admits an infinite linearly independent set
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T20%3A18%3A57IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=The%200-concordance%20monoid%20admits%20an%20infinite%20linearly%20independent%20set&rft.jtitle=arXiv.org&rft.au=Dai,%20Irving&rft.date=2023-09-03&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2259089550%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_22590895503%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2259089550&rft_id=info:pmid/&rfr_iscdi=true