<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-01571382</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-24T20:32:35+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">ON THE SMOOTH WHITNEY FIBERING CONJECTURE</title>
            <author role="aut">
              <persName>
                <forename type="first">C</forename>
                <surname>Murolo</surname>
              </persName>
              <idno type="halauthorid">1055532-0</idno>
              <affiliation ref="#struct-241321"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">A</forename>
                <forename type="middle">A</forename>
                <surname>Du Plessis</surname>
              </persName>
              <email type="md5">8470bf09739fe440ac1d4c588cd47718</email>
              <email type="domain">math.au.dk</email>
              <idno type="idhal" notation="numeric">1014143</idno>
              <idno type="halauthorid" notation="string">1208334-1014143</idno>
              <affiliation ref="#struct-53308"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">D</forename>
                <forename type="middle">J A</forename>
                <surname>Trotman</surname>
              </persName>
              <idno type="halauthorid">1208335-0</idno>
              <affiliation ref="#struct-241321"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>David</forename>
                <surname>Trotman</surname>
              </persName>
              <email type="md5">b019e98ec6666d9b3b07bd783311d826</email>
              <email type="domain">univ-amu.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2017-08-02 12:04:16</date>
              <date type="whenWritten">2017-07-28</date>
              <date type="whenModified">2024-04-30 16:08:43</date>
              <date type="whenReleased">2017-08-07 11:33:49</date>
              <date type="whenProduced">2017-07-28</date>
              <date type="whenEndEmbargoed">2017-08-02</date>
              <ref type="file" target="https://hal.science/hal-01571382v1/document">
                <date notBefore="2017-08-02"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-01571382v1/file/CFW-WFC-28-07-2017.pdf" id="file-1571382-1625841">
                <date notBefore="2017-08-02"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="331417">
                <persName>
                  <forename>David</forename>
                  <surname>Trotman</surname>
                </persName>
                <email type="md5">b019e98ec6666d9b3b07bd783311d826</email>
                <email type="domain">univ-amu.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01571382</idno>
            <idno type="halUri">https://hal.science/hal-01571382</idno>
            <idno type="halBibtex">murolo:hal-01571382</idno>
            <idno type="halRefHtml">2017</idno>
            <idno type="halRef">2017</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1571382-1625841"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="EC-MARSEILLE">Ecole Centrale de Marseille</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="I2M">Institut de Mathématiques de Marseille</idno>
            <idno type="stamp" n="I2M-2014-" corresp="I2M">Institut de Mathématiques de Marseille 2014-</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">Nouvelle version avec changement de titre et matériel supplémentaire du preprint "The smooth Whitney fibering conjecture and open books in Whitney and Bekka stratifications" (2016).</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">ON THE SMOOTH WHITNEY FIBERING CONJECTURE</title>
                <author role="aut">
                  <persName>
                    <forename type="first">C</forename>
                    <surname>Murolo</surname>
                  </persName>
                  <idno type="halauthorid">1055532-0</idno>
                  <affiliation ref="#struct-241321"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">A</forename>
                    <forename type="middle">A</forename>
                    <surname>Du Plessis</surname>
                  </persName>
                  <email type="md5">8470bf09739fe440ac1d4c588cd47718</email>
                  <email type="domain">math.au.dk</email>
                  <idno type="idhal" notation="numeric">1014143</idno>
                  <idno type="halauthorid" notation="string">1208334-1014143</idno>
                  <affiliation ref="#struct-53308"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">D</forename>
                    <forename type="middle">J A</forename>
                    <surname>Trotman</surname>
                  </persName>
                  <idno type="halauthorid">1208335-0</idno>
                  <affiliation ref="#struct-241321"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <relatedItem target="https://hal.science/hal-01359601v1" type="IsVersionOf" subtype="http://purl.org/coar/resource_type/c_816b">Titre changé et section rajoutée.</relatedItem>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Topologically stable maps</term>
                <term xml:lang="en">Wings</term>
                <term xml:lang="en">Whitney fibering conjecture</term>
                <term xml:lang="en">Bekka (c)-regularity</term>
                <term xml:lang="en">Whitney conditions</term>
              </keywords>
              <classCode scheme="classification">MSC 58</classCode>
              <classCode scheme="halDomain" n="math.math-gt">Mathematics [math]/Geometric Topology [math.GT]</classCode>
              <classCode scheme="halDomain" n="math.math-dg">Mathematics [math]/Differential Geometry [math.DG]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We improve upon the first Thom-Mather isotopy theorem for Whitney stratified sets. In particular , for the more general Bekka stratified sets we show that there is a local foliated structure with continuously varying tangent spaces, thus proving the smooth version of the Whitney fiber-ing conjecture. A regular wing structure is also shown to exist locally, for both Whitney and Bekka stratifications. The proofs involve integrating carefully chosen controlled distributions of vector fields. As an application of our main theorem we show the density of the subset of strongly topologically stable mappings in the space of all smooth quasi-proper mappings between smooth manifolds, an improvement of a theorem of Mather. </p>
            </abstract>
            <abstract xml:lang="fr">
              <p>Nous améliorons le premier théorème d'isotopie de Thom-Mather pour les ensembles stratifiés de Whitney. En  particulier pour les ensembles stratifiés de Bekka, plus généraux, nous montrons qu'il a une structure feuilletée locale avec des espaces tangents variant continûment, ainsi démontrant la version lisse de la conjecture de fibration de Whitney.  Une structure d'ailes régulières est aussi démontrée localement pour des stratifications de Whitney et de Bekka. Les preuves nécessitent l'intégration de distributions de champs de vecteurs contrôlées soigneusement choisies. Comme une application de notre théorème principal nous montrons la densité du sou-ensemble des applications fortement topologiquement stables dans l'espace des applications lisses quasi-propes entre deux variétés lisses, un renforcement d'un théorème de Mather.  </p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-241321" status="VALID">
          <idno type="RNSR">201420768T</idno>
          <idno type="ROR">042h2y225</idno>
          <orgName>Institut de Mathématiques de Marseille</orgName>
          <orgName type="acronym">I2M</orgName>
          <date type="start">2014</date>
          <desc>
            <address>
              <addrLine>Centre de Mathématiques et Informatique (CMI)Technopôle Château-Gombert39, rue Frédéric Joliot Curie13453 Marseille Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.i2m.univ-amu.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR7373" active="#struct-198056" type="direct"/>
            <relation name="UMR7373" active="#struct-300415" type="direct"/>
            <relation name="UMR7373" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-53308" status="INCOMING">
          <orgName>Insitut for Matematiske fag</orgName>
          <desc>
            <address>
              <country key="DK"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-19908" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-198056" status="VALID">
          <idno type="IdRef">15863621X</idno>
          <idno type="ISNI">0000 0001 2176 4817</idno>
          <idno type="ROR">https://ror.org/035xkbk20</idno>
          <orgName>Aix Marseille Université</orgName>
          <orgName type="acronym">AMU</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Aix-Marseille UniversitéJardins du Pharo58 Boulevard Charles Livon13284 Marseille cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-amu.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300415" status="VALID">
          <idno type="ISNI">0000 0004 1762 2703</idno>
          <idno type="ROR">https://ror.org/040baw385</idno>
          <orgName>École Centrale de Marseille</orgName>
          <orgName type="acronym">ECM</orgName>
          <date type="start">2006-09-27</date>
          <desc>
            <address>
              <addrLine>Pôle de l'étoile - Technopole de Château-Gombert - 38 rue Frédéric Joliot-Curie - 13013 Marseille</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.centrale-marseille.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-19908" status="VALID">
          <idno type="IdRef">026461307</idno>
          <idno type="ROR">https://ror.org/01aj84f44</idno>
          <orgName>Aarhus University [Aarhus]</orgName>
          <desc>
            <address>
              <addrLine>Nordre Ringgade 1 DK-8000 Aarhus C</addrLine>
              <country key="DK"/>
            </address>
            <ref type="url">http://www.au.dk/en/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>