The fundamental group of manifolds of positive isotropic curvature and surface groups

In this article, we study the topology of compact manifolds with positive isotropic curvature (PIC). There are many examples of nonsimply connected compact manifolds with PIC. We prove that the fundamental group of a compact Riemannian manifold of dimension at least 5 with PIC does not contain a sub...

Full description

Saved in:
Bibliographic Details
Published in:Duke mathematical journal 2006-06, Vol.133 (2), p.325-334
Main Authors: Fraser, Ailana, Wolfson, Jon
Format: Article
Language:English
Subjects:
53C21
58E12
Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]
curvature restrictions [See also 58J60]
including PDE methods
Methods of Riemannian geometry
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c348t-ce6f92335f5fdccf598fda9b94207096292b9a0fa0f3da2003a957d3e7214a6b3
cites cdi_FETCH-LOGICAL-c348t-ce6f92335f5fdccf598fda9b94207096292b9a0fa0f3da2003a957d3e7214a6b3
container_end_page 334
container_issue 2
container_start_page 325
container_title Duke mathematical journal
container_volume 133
creator Fraser, Ailana
Wolfson, Jon
description In this article, we study the topology of compact manifolds with positive isotropic curvature (PIC). There are many examples of nonsimply connected compact manifolds with PIC. We prove that the fundamental group of a compact Riemannian manifold of dimension at least 5 with PIC does not contain a subgroup isomorphic to the fundamental group of a compact Riemann surface. The proof uses stable minimal surface theory
doi_str_mv 10.1215/S0012-7094-06-13325-2
format article
fullrecord <record><control><sourceid>istex_proje</sourceid><recordid>TN_cdi_projecteuclid_primary_oai_CULeuclid_euclid_dmj_1148224042</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>ark_67375_765_4T3KFPKC_3</sourcerecordid><originalsourceid>FETCH-LOGICAL-c348t-ce6f92335f5fdccf598fda9b94207096292b9a0fa0f3da2003a957d3e7214a6b3</originalsourceid><addsrcrecordid>eNo9kG1LwzAUhYMoOKc_QegfiOa1bb4pxalsoOD2OWR50cy2KUkr-u9d1zG4cDiX-xwuB4BbjO4wwfz-AyFMYIEEgyiHmFLCITkDM8xZAQsqynMwO51cgquUdqMVOZmBzfrLZm5ojWps26s6-4xh6LLgska13oXapNF0Ifne_9jMp9DH0Hmd6SH-qH6INlOtydIQndJ2wtM1uHCqTvbmqHOwWTytqxe4ent-rR5XUFNW9lDb3AlCKXfcGa0dF6UzSmwFI2j_a04E2QqF3H6oUQQhqgQvDLUFwUzlWzoHD1NuF8PO6t4OuvZGdtE3Kv7JoLysNqvj9iim2UmMWUkIQ4zsI_gUoWNIKVp3ojGSY73yUK8cu5Mol4d65cjBifOpt78nSMVvmRe04LLIuWRruly8LytJ6T8hX371</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>The fundamental group of manifolds of positive isotropic curvature and surface groups</title><source>Project Euclid Complete</source><creator>Fraser, Ailana ; Wolfson, Jon</creator><creatorcontrib>Fraser, Ailana ; Wolfson, Jon</creatorcontrib><description>In this article, we study the topology of compact manifolds with positive isotropic curvature (PIC). There are many examples of nonsimply connected compact manifolds with PIC. We prove that the fundamental group of a compact Riemannian manifold of dimension at least 5 with PIC does not contain a subgroup isomorphic to the fundamental group of a compact Riemann surface. The proof uses stable minimal surface theory</description><identifier>ISSN: 0012-7094</identifier><identifier>EISSN: 1547-7398</identifier><identifier>DOI: 10.1215/S0012-7094-06-13325-2</identifier><language>eng</language><publisher>DUKE University Press</publisher><subject>53C21 ; 58E12 ; Applications to minimal surfaces (problems in two independent variables) [See also 49Q05] ; curvature restrictions [See also 58J60] ; including PDE methods ; Methods of Riemannian geometry</subject><ispartof>Duke mathematical journal, 2006-06, Vol.133 (2), p.325-334</ispartof><rights>Copyright 2006 Duke University Press</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c348t-ce6f92335f5fdccf598fda9b94207096292b9a0fa0f3da2003a957d3e7214a6b3</citedby><cites>FETCH-LOGICAL-c348t-ce6f92335f5fdccf598fda9b94207096292b9a0fa0f3da2003a957d3e7214a6b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,926,27924,27925</link.rule.ids></links><search><creatorcontrib>Fraser, Ailana</creatorcontrib><creatorcontrib>Wolfson, Jon</creatorcontrib><title>The fundamental group of manifolds of positive isotropic curvature and surface groups</title><title>Duke mathematical journal</title><description>In this article, we study the topology of compact manifolds with positive isotropic curvature (PIC). There are many examples of nonsimply connected compact manifolds with PIC. We prove that the fundamental group of a compact Riemannian manifold of dimension at least 5 with PIC does not contain a subgroup isomorphic to the fundamental group of a compact Riemann surface. The proof uses stable minimal surface theory</description><subject>53C21</subject><subject>58E12</subject><subject>Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]</subject><subject>curvature restrictions [See also 58J60]</subject><subject>including PDE methods</subject><subject>Methods of Riemannian geometry</subject><issn>0012-7094</issn><issn>1547-7398</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNo9kG1LwzAUhYMoOKc_QegfiOa1bb4pxalsoOD2OWR50cy2KUkr-u9d1zG4cDiX-xwuB4BbjO4wwfz-AyFMYIEEgyiHmFLCITkDM8xZAQsqynMwO51cgquUdqMVOZmBzfrLZm5ojWps26s6-4xh6LLgska13oXapNF0Ifne_9jMp9DH0Hmd6SH-qH6INlOtydIQndJ2wtM1uHCqTvbmqHOwWTytqxe4ent-rR5XUFNW9lDb3AlCKXfcGa0dF6UzSmwFI2j_a04E2QqF3H6oUQQhqgQvDLUFwUzlWzoHD1NuF8PO6t4OuvZGdtE3Kv7JoLysNqvj9iim2UmMWUkIQ4zsI_gUoWNIKVp3ojGSY73yUK8cu5Mol4d65cjBifOpt78nSMVvmRe04LLIuWRruly8LytJ6T8hX371</recordid><startdate>20060601</startdate><enddate>20060601</enddate><creator>Fraser, Ailana</creator><creator>Wolfson, Jon</creator><general>DUKE University Press</general><general>Duke University Press</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20060601</creationdate><title>The fundamental group of manifolds of positive isotropic curvature and surface groups</title><author>Fraser, Ailana ; Wolfson, Jon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c348t-ce6f92335f5fdccf598fda9b94207096292b9a0fa0f3da2003a957d3e7214a6b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>53C21</topic><topic>58E12</topic><topic>Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]</topic><topic>curvature restrictions [See also 58J60]</topic><topic>including PDE methods</topic><topic>Methods of Riemannian geometry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fraser, Ailana</creatorcontrib><creatorcontrib>Wolfson, Jon</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>Duke mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fraser, Ailana</au><au>Wolfson, Jon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The fundamental group of manifolds of positive isotropic curvature and surface groups</atitle><jtitle>Duke mathematical journal</jtitle><date>2006-06-01</date><risdate>2006</risdate><volume>133</volume><issue>2</issue><spage>325</spage><epage>334</epage><pages>325-334</pages><issn>0012-7094</issn><eissn>1547-7398</eissn><abstract>In this article, we study the topology of compact manifolds with positive isotropic curvature (PIC). There are many examples of nonsimply connected compact manifolds with PIC. We prove that the fundamental group of a compact Riemannian manifold of dimension at least 5 with PIC does not contain a subgroup isomorphic to the fundamental group of a compact Riemann surface. The proof uses stable minimal surface theory</abstract><pub>DUKE University Press</pub><doi>10.1215/S0012-7094-06-13325-2</doi><tpages>10</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0012-7094
ispartof Duke mathematical journal, 2006-06, Vol.133 (2), p.325-334
issn 0012-7094
1547-7398
language eng
recordid cdi_projecteuclid_primary_oai_CULeuclid_euclid_dmj_1148224042
source Project Euclid Complete
subjects 53C21
58E12
Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]
curvature restrictions [See also 58J60]
including PDE methods
Methods of Riemannian geometry
title The fundamental group of manifolds of positive isotropic curvature and surface groups
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T22%3A52%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-istex_proje&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20fundamental%20group%20of%20manifolds%20of%20positive%20isotropic%20curvature%20and%20surface%20groups&rft.jtitle=Duke%20mathematical%20journal&rft.au=Fraser,%20Ailana&rft.date=2006-06-01&rft.volume=133&rft.issue=2&rft.spage=325&rft.epage=334&rft.pages=325-334&rft.issn=0012-7094&rft.eissn=1547-7398&rft_id=info:doi/10.1215/S0012-7094-06-13325-2&rft_dat=%3Cistex_proje%3Eark_67375_765_4T3KFPKC_3%3C/istex_proje%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c348t-ce6f92335f5fdccf598fda9b94207096292b9a0fa0f3da2003a957d3e7214a6b3%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