<?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-02196781</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="2026-05-03T00:22:44+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Stated skein algebras of surfaces</title>
            <author role="aut">
              <persName>
                <forename type="first">Francesco</forename>
                <surname>Costantino</surname>
              </persName>
              <idno type="halauthorid">157247-0</idno>
              <affiliation ref="#struct-1954"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Thang</forename>
                <surname>Lê</surname>
              </persName>
              <idno type="halauthorid">3375065-0</idno>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Francesco</forename>
                <surname>Costantino</surname>
              </persName>
              <email type="md5">2a0880480acc13613fc6fc7b09da454e</email>
              <email type="domain">math.univ-toulouse.fr</email>
            </editor>
            <funder ref="#projanr-44738"/>
            <funder ref="#projanr-49786"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2019-07-29 15:12:14</date>
              <date type="whenModified">2026-01-14 10:59:58</date>
              <date type="whenReleased">2019-07-29 15:12:14</date>
              <date type="whenProduced">2022-07-13</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/1907.11400"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="117073">
                <persName>
                  <forename>Francesco</forename>
                  <surname>Costantino</surname>
                </persName>
                <email type="md5">2a0880480acc13613fc6fc7b09da454e</email>
                <email type="domain">math.univ-toulouse.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-02196781</idno>
            <idno type="halUri">https://hal.science/hal-02196781</idno>
            <idno type="halBibtex">costantino:hal-02196781</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of the European Mathematical Society&lt;/i&gt;, 2022, 24 (12), pp.4063-4142. &lt;a target="_blank" href="https://dx.doi.org/10.4171/JEMS/1167"&gt;&amp;#x27E8;10.4171/JEMS/1167&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of the European Mathematical Society, 2022, 24 (12), pp.4063-4142. &amp;#x27E8;10.4171/JEMS/1167&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-TLSE2">Université Toulouse 2</idno>
            <idno type="stamp" n="UNIV-TLSE3">Université de Toulouse</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSA-TOULOUSE">Institut National des Sciences Appliquées de Toulouse</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="IMT">Institut de Mathématiques de Toulouse</idno>
            <idno type="stamp" n="UT1-CAPITOLE">Université Toulouse 1 Capitole</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="TEST-HALCNRS">Collection test HAL CNRS</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="CIMI-TOULOUSE">Centre International de Mathématiques et d'Informatique de Toulouse</idno>
            <idno type="stamp" n="UNIV-UT3">Université Toulouse 3</idno>
            <idno type="stamp" n="UT3-INP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="UT3-TOULOUSEINP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="ANR_QUANTIQUE">ANR QUANTIQUE</idno>
            <idno type="stamp" n="ANR_QUANTIQUE_1" corresp="ANR_QUANTIQUE">ANR_QUANTIQUE_1</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">68 pages, 29 figures</note>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Stated skein algebras of surfaces</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Francesco</forename>
                    <surname>Costantino</surname>
                  </persName>
                  <idno type="halauthorid">157247-0</idno>
                  <affiliation ref="#struct-1954"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Thang</forename>
                    <surname>Lê</surname>
                  </persName>
                  <idno type="halauthorid">3375065-0</idno>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">16350</idno>
                <idno type="issn">1435-9855</idno>
                <idno type="eissn">1435-9863</idno>
                <title level="j">Journal of the European Mathematical Society</title>
                <imprint>
                  <publisher>European Mathematical Society</publisher>
                  <biblScope unit="volume">24</biblScope>
                  <biblScope unit="issue">12</biblScope>
                  <biblScope unit="pp">4063-4142</biblScope>
                  <date type="datePub">2022-07-13</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1907.11400</idno>
              <idno type="doi">10.4171/JEMS/1167</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-gt">Mathematics [math]/Geometric Topology [math.GT]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We study the algebraic and geometric properties of stated skein algebras of surfaces with punctured boundary. We prove that the skein algebra of the bigon is isomorphic to the quantum group ${\mathcal O}_{q^2}(\mathrm{SL}(2))$ providing a topological interpretation for its structure morphisms. We also show that its stated skein algebra lifts in a suitable sense the Reshetikhin-Turaev functor and in particular we recover the dual $R$-matrix for ${\mathcal O}_{q^2}(\mathrm{SL}(2))$ in a topological way. We deduce that the skein algebra of a surface with $n$ boundary components is an algebra-comodule over ${\mathcal O}_{q^2}(\mathrm{SL}(2))^{\otimes{n}}$ and prove that cutting along an ideal arc corresponds to Hochshild cohomology of bicomodules. We give a topological interpretation of braided tensor product of stated skein algebras of surfaces as "glueing on a triangle"; then we recover topologically some braided bialgebras in the category of ${\mathcal O}_{q^2}(\mathrm{SL}(2))$-comodules, among which the "transmutation" of ${\mathcal O}_{q^2}(\mathrm{SL}(2))$. We also provide an operadic interpretation of stated skein algebras as an example of a "geometric non symmetric modular operad". In the last part of the paper we define a reduced version of stated skein algebras and prove that it allows to recover Bonahon-Wong's quantum trace map and interpret skein algebras in the classical limit when $q\to 1$ as regular functions over a suitable version of moduli spaces of twisted bundles.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-1954" status="OLD">
          <idno type="IdRef">166783900</idno>
          <idno type="ISNI">0000000403836348</idno>
          <idno type="RNSR">200711888W</idno>
          <idno type="ROR">https://ror.org/014vp6c30</idno>
          <orgName>Institut de Mathématiques de Toulouse UMR5219</orgName>
          <orgName type="acronym">IMT</orgName>
          <date type="start">2007-01-01</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>UPS IMT, F-31062 Toulouse Cedex 9, INSA Toulouse, F-31077 Toulouse,France UT1, F-31042 Toulouse, France UT2, F-31058 Toulouse,Téléphone : 05.61.55.67.90</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.math.univ-toulouse.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-81148" type="direct"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116255" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-217752" type="direct"/>
            <relation name="UMR5219" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-81148" status="VALID">
          <idno type="IdRef">026404354</idno>
          <idno type="ISNI">0000000121902837</idno>
          <idno type="ROR">https://ror.org/0443n9e75</idno>
          <orgName>Université Toulouse Capitole</orgName>
          <orgName type="acronym">UT Capitole</orgName>
          <date type="start">1970-01-01</date>
          <desc>
            <address>
              <addrLine>2 rue du Doyen-Gabriel-Marty - 31042 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ut-capitole.fr/</ref>
          </desc>
          <listRelation>
            <relation name="443875" active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-443875" status="VALID">
          <idno type="ROR">https://ror.org/017tgbk05</idno>
          <orgName>Communauté d'universités et établissements de Toulouse</orgName>
          <orgName type="acronym">Comue de Toulouse</orgName>
          <desc>
            <address>
              <addrLine>41 Allée Jules Guesde, 31000 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-toulouse.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116255" status="VALID">
          <idno type="IdRef">026388766</idno>
          <idno type="ISNI">0000 0001 2286 8343</idno>
          <idno type="ROR">https://ror.org/01h8pf755</idno>
          <idno type="Wikidata">Q858979</idno>
          <orgName>Institut National des Sciences Appliquées - Toulouse</orgName>
          <orgName type="acronym">INSA Toulouse</orgName>
          <date type="start">1963-10-21</date>
          <desc>
            <address>
              <addrLine>135, avenue de Rangueil - 31077 Toulouse cedex 4</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-toulouse.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301232" type="direct"/>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116256" status="VALID">
          <idno type="IdRef">026403994</idno>
          <idno type="ROR">https://ror.org/04ezk3x31</idno>
          <orgName>Université Toulouse - Jean Jaurès</orgName>
          <orgName type="acronym">UT2J</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>5 allées Antonio Machado - 31058 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse2.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-217752" status="OLD">
          <idno type="IdRef">026404672</idno>
          <idno type="ISNI">0000000121617331</idno>
          <idno type="ROR">https://ror.org/02v6kpv12</idno>
          <idno type="Wikidata">Q1273188</idno>
          <orgName>Université Toulouse III - Paul Sabatier</orgName>
          <orgName type="acronym">UT3</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 route de Narbonne - 31062 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse3.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </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>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-44738" status="VALID">
          <idno type="anr">ANR-16-CE40-0017</idno>
          <orgName>Quantact</orgName>
          <desc>Topologie quantique et géométrie de contact</desc>
          <date type="start">2016</date>
        </org>
        <org type="anrProject" xml:id="projanr-49786" status="VALID">
          <idno type="anr">ANR-11-LABX-0040</idno>
          <orgName>CIMI</orgName>
          <desc>Centre International de Mathématiques et d'Informatique (de Toulouse)</desc>
          <date type="start">2011</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>