Covering group theory for topological groups
Identifieur interne : 001300 ( Main/Merge ); précédent : 001299; suivant : 001301Covering group theory for topological groups
Auteurs : Valera Berestovskii [Russie] ; Conrad Plaut [États-Unis]Source :
- Topology and its Applications [ 0166-8641 ] ; 2001.
English descriptors
- KwdEn :
- 22A05, 55Q05, 57T20, Arcwise, Berestovskii, Chevalley, Commutativity, Commutativity relation, Compact groups, Connectedness, Continuous function, Corollary, Countable, Coverable, Coverable group, Coverable groups, Dense subgroup, Direct product, Discrete kernel, Epimorphism, Epimorphisms, Equivalence class, Fundamental group, Group theory, Homeomorphism, Homomorphism, Homotopic, Homotopy, Injective, Inverse limit, Inverse limits, Inverse system, Isomorphic, Isomorphism, Lemma, Local group, Local group isomorphism, Local isomorphism, Metrizable, Natural epimorphism, Natural homomorphism, Natural homomorphisms, Natural projection, Next lemma, Nite, Normal subgroup, Open epimorphism, Open homomorphism, Open neighborhood, Open subgroup, Open surjection, Other words, Plaut, Plaut topology, Prodiscrete, Quotient, Schreier, Schreier group, Schreier groups, Semilocally, Subgroup, Subset, Surjection, Surjective, Symmetric neighborhood, Symmetric neighborhoods, Tit, Topological, Topological group, Topological groups, Topological space, Topological spaces, Topology, Unique homomorphism, Unique isomorphism, Universal cover, Universal property.
- Teeft :
- Arcwise, Berestovskii, Chevalley, Commutativity, Commutativity relation, Compact groups, Connectedness, Continuous function, Corollary, Countable, Coverable, Coverable group, Coverable groups, Dense subgroup, Direct product, Discrete kernel, Epimorphism, Epimorphisms, Equivalence class, Fundamental group, Group theory, Homeomorphism, Homomorphism, Homotopic, Homotopy, Injective, Inverse limit, Inverse limits, Inverse system, Isomorphic, Isomorphism, Lemma, Local group, Local group isomorphism, Local isomorphism, Metrizable, Natural epimorphism, Natural homomorphism, Natural homomorphisms, Natural projection, Next lemma, Nite, Normal subgroup, Open epimorphism, Open homomorphism, Open neighborhood, Open subgroup, Open surjection, Other words, Plaut, Plaut topology, Prodiscrete, Quotient, Schreier, Schreier group, Schreier groups, Semilocally, Subgroup, Subset, Surjection, Surjective, Symmetric neighborhood, Symmetric neighborhoods, Tit, Topological, Topological group, Topological groups, Topological space, Topological spaces, Topology, Unique homomorphism, Unique isomorphism, Universal property.
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
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ISTEX:9E3D79BC76F0C92174D22A8548EF4B34248D2AEELe document en format XML
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<term>Berestovskii</term>
<term>Chevalley</term>
<term>Commutativity</term>
<term>Commutativity relation</term>
<term>Compact groups</term>
<term>Connectedness</term>
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<term>Corollary</term>
<term>Countable</term>
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<term>Inverse limits</term>
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<term>Connectedness</term>
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<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>
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<term>Isomorphism</term>
<term>Lemma</term>
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<term>Local isomorphism</term>
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<term>Natural homomorphism</term>
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<term>Natural projection</term>
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<term>Surjective</term>
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<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>
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