Serveur d'exploration Bourbaki

Attention, ce site est en cours de développement !
Attention, site généré par des moyens informatiques à partir de corpus bruts.
Les informations ne sont donc pas validées.

Covering group theory for topological groups

Identifieur interne : 001300 ( Main/Merge ); précédent : 001299; suivant : 001301

Covering group theory for topological groups

Auteurs : Valera Berestovskii [Russie] ; Conrad Plaut [États-Unis]

Source :

RBID : ISTEX:9E3D79BC76F0C92174D22A8548EF4B34248D2AEE

English descriptors

Abstract

Abstract: We develop a covering group theory for a large category of “coverable” topological groups, with a generalized notion of “cover”. Coverable groups include, for example, all metrizable, connected, locally connected groups, and even many totally disconnected groups. Our covering group theory produces a categorial notion of fundamental group, which, in contrast to traditional theory, is naturally a (prodiscrete) topological group. Central to our work is a link between the fundamental group and global extension properties of local group homomorphisms. We provide methods for computing the fundamental group of inverse limits and dense subgroups or completions of coverable groups. Our theory includes as special cases the traditional theory of Poincaré, as well as alternative theories due to Chevalley, Tits, and Hoffmann–Morris. We include a number of examples and open problems.

Url:
DOI: 10.1016/S0166-8641(00)00031-6

Links toward previous steps (curation, corpus...)


Links to Exploration step

ISTEX:9E3D79BC76F0C92174D22A8548EF4B34248D2AEE

Le document en format XML

<record>
<TEI wicri:istexFullTextTei="biblStruct">
<teiHeader>
<fileDesc>
<titleStmt>
<title xml:lang="en">Covering group theory for topological groups</title>
<author>
<name sortKey="Berestovskii, Valera" sort="Berestovskii, Valera" uniqKey="Berestovskii V" first="Valera" last="Berestovskii">Valera Berestovskii</name>
</author>
<author>
<name sortKey="Plaut, Conrad" sort="Plaut, Conrad" uniqKey="Plaut C" first="Conrad" last="Plaut">Conrad Plaut</name>
</author>
</titleStmt>
<publicationStmt>
<idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:9E3D79BC76F0C92174D22A8548EF4B34248D2AEE</idno>
<date when="2001" year="2001">2001</date>
<idno type="doi">10.1016/S0166-8641(00)00031-6</idno>
<idno type="url">https://api.istex.fr/document/9E3D79BC76F0C92174D22A8548EF4B34248D2AEE/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">002038</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002038</idno>
<idno type="wicri:Area/Istex/Curation">002038</idno>
<idno type="wicri:Area/Istex/Checkpoint">001161</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">001161</idno>
<idno type="wicri:doubleKey">0166-8641:2001:Berestovskii V:covering:group:theory</idno>
<idno type="wicri:Area/Main/Merge">001300</idno>
</publicationStmt>
<sourceDesc>
<biblStruct>
<analytic>
<title level="a" type="main" xml:lang="en">Covering group theory for topological groups</title>
<author>
<name sortKey="Berestovskii, Valera" sort="Berestovskii, Valera" uniqKey="Berestovskii V" first="Valera" last="Berestovskii">Valera Berestovskii</name>
<affiliation wicri:level="1">
<country xml:lang="fr">Russie</country>
<wicri:regionArea>Department of Mathematics, Omsk State University, Pr. Mira 55A, Omsk 77</wicri:regionArea>
<wicri:noRegion>Omsk 77</wicri:noRegion>
</affiliation>
<affiliation></affiliation>
</author>
<author>
<name sortKey="Plaut, Conrad" sort="Plaut, Conrad" uniqKey="Plaut C" first="Conrad" last="Plaut">Conrad Plaut</name>
<affiliation wicri:level="2">
<country xml:lang="fr">États-Unis</country>
<wicri:regionArea>Department of Mathematics, University of Tennessee, Knoxville, TN 37919</wicri:regionArea>
<placeName>
<region type="state">Tennessee</region>
</placeName>
</affiliation>
<affiliation></affiliation>
<affiliation wicri:level="1">
<country wicri:rule="url">États-Unis</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series>
<title level="j">Topology and its Applications</title>
<title level="j" type="abbrev">TOPOL</title>
<idno type="ISSN">0166-8641</idno>
<imprint>
<publisher>ELSEVIER</publisher>
<date type="published" when="2001">2001</date>
<biblScope unit="volume">114</biblScope>
<biblScope unit="issue">2</biblScope>
<biblScope unit="page" from="141">141</biblScope>
<biblScope unit="page" to="186">186</biblScope>
</imprint>
<idno type="ISSN">0166-8641</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt>
<idno type="ISSN">0166-8641</idno>
</seriesStmt>
</fileDesc>
<profileDesc>
<textClass>
<keywords scheme="KwdEn" xml:lang="en">
<term>22A05</term>
<term>55Q05</term>
<term>57T20</term>
<term>Arcwise</term>
<term>Berestovskii</term>
<term>Chevalley</term>
<term>Commutativity</term>
<term>Commutativity relation</term>
<term>Compact groups</term>
<term>Connectedness</term>
<term>Continuous function</term>
<term>Corollary</term>
<term>Countable</term>
<term>Coverable</term>
<term>Coverable group</term>
<term>Coverable groups</term>
<term>Dense subgroup</term>
<term>Direct product</term>
<term>Discrete kernel</term>
<term>Epimorphism</term>
<term>Epimorphisms</term>
<term>Equivalence class</term>
<term>Fundamental group</term>
<term>Group theory</term>
<term>Homeomorphism</term>
<term>Homomorphism</term>
<term>Homotopic</term>
<term>Homotopy</term>
<term>Injective</term>
<term>Inverse limit</term>
<term>Inverse limits</term>
<term>Inverse system</term>
<term>Isomorphic</term>
<term>Isomorphism</term>
<term>Lemma</term>
<term>Local group</term>
<term>Local group isomorphism</term>
<term>Local isomorphism</term>
<term>Metrizable</term>
<term>Natural epimorphism</term>
<term>Natural homomorphism</term>
<term>Natural homomorphisms</term>
<term>Natural projection</term>
<term>Next lemma</term>
<term>Nite</term>
<term>Normal subgroup</term>
<term>Open epimorphism</term>
<term>Open homomorphism</term>
<term>Open neighborhood</term>
<term>Open subgroup</term>
<term>Open surjection</term>
<term>Other words</term>
<term>Plaut</term>
<term>Plaut topology</term>
<term>Prodiscrete</term>
<term>Quotient</term>
<term>Schreier</term>
<term>Schreier group</term>
<term>Schreier groups</term>
<term>Semilocally</term>
<term>Subgroup</term>
<term>Subset</term>
<term>Surjection</term>
<term>Surjective</term>
<term>Symmetric neighborhood</term>
<term>Symmetric neighborhoods</term>
<term>Tit</term>
<term>Topological</term>
<term>Topological group</term>
<term>Topological groups</term>
<term>Topological space</term>
<term>Topological spaces</term>
<term>Topology</term>
<term>Unique homomorphism</term>
<term>Unique isomorphism</term>
<term>Universal cover</term>
<term>Universal property</term>
</keywords>
<keywords scheme="Teeft" xml:lang="en">
<term>Arcwise</term>
<term>Berestovskii</term>
<term>Chevalley</term>
<term>Commutativity</term>
<term>Commutativity relation</term>
<term>Compact groups</term>
<term>Connectedness</term>
<term>Continuous function</term>
<term>Corollary</term>
<term>Countable</term>
<term>Coverable</term>
<term>Coverable group</term>
<term>Coverable groups</term>
<term>Dense subgroup</term>
<term>Direct product</term>
<term>Discrete kernel</term>
<term>Epimorphism</term>
<term>Epimorphisms</term>
<term>Equivalence class</term>
<term>Fundamental group</term>
<term>Group theory</term>
<term>Homeomorphism</term>
<term>Homomorphism</term>
<term>Homotopic</term>
<term>Homotopy</term>
<term>Injective</term>
<term>Inverse limit</term>
<term>Inverse limits</term>
<term>Inverse system</term>
<term>Isomorphic</term>
<term>Isomorphism</term>
<term>Lemma</term>
<term>Local group</term>
<term>Local group isomorphism</term>
<term>Local isomorphism</term>
<term>Metrizable</term>
<term>Natural epimorphism</term>
<term>Natural homomorphism</term>
<term>Natural homomorphisms</term>
<term>Natural projection</term>
<term>Next lemma</term>
<term>Nite</term>
<term>Normal subgroup</term>
<term>Open epimorphism</term>
<term>Open homomorphism</term>
<term>Open neighborhood</term>
<term>Open subgroup</term>
<term>Open surjection</term>
<term>Other words</term>
<term>Plaut</term>
<term>Plaut topology</term>
<term>Prodiscrete</term>
<term>Quotient</term>
<term>Schreier</term>
<term>Schreier group</term>
<term>Schreier groups</term>
<term>Semilocally</term>
<term>Subgroup</term>
<term>Subset</term>
<term>Surjection</term>
<term>Surjective</term>
<term>Symmetric neighborhood</term>
<term>Symmetric neighborhoods</term>
<term>Tit</term>
<term>Topological</term>
<term>Topological group</term>
<term>Topological groups</term>
<term>Topological space</term>
<term>Topological spaces</term>
<term>Topology</term>
<term>Unique homomorphism</term>
<term>Unique isomorphism</term>
<term>Universal property</term>
</keywords>
</textClass>
<langUsage>
<language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front>
<div type="abstract" xml:lang="en">Abstract: We develop a covering group theory for a large category of “coverable” topological groups, with a generalized notion of “cover”. Coverable groups include, for example, all metrizable, connected, locally connected groups, and even many totally disconnected groups. Our covering group theory produces a categorial notion of fundamental group, which, in contrast to traditional theory, is naturally a (prodiscrete) topological group. Central to our work is a link between the fundamental group and global extension properties of local group homomorphisms. We provide methods for computing the fundamental group of inverse limits and dense subgroups or completions of coverable groups. Our theory includes as special cases the traditional theory of Poincaré, as well as alternative theories due to Chevalley, Tits, and Hoffmann–Morris. We include a number of examples and open problems.</div>
</front>
</TEI>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Merge
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 001300 | SxmlIndent | more

Ou

HfdSelect -h $EXPLOR_AREA/Data/Main/Merge/biblio.hfd -nk 001300 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Mathematiques
   |area=    BourbakiV1
   |flux=    Main
   |étape=   Merge
   |type=    RBID
   |clé=     ISTEX:9E3D79BC76F0C92174D22A8548EF4B34248D2AEE
   |texte=   Covering group theory for topological groups
}}

Wicri

This area was generated with Dilib version V0.6.33.
Data generation: Thu Jul 5 10:00:31 2018. Site generation: Sat Nov 19 17:42:07 2022