About: Bass–Serre theory

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Bass–Serre theory Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FBass%E2%80%93Serre_theory&invfp=IFP_OFF&sas=SAME_AS_OFF

Bass–Serre theory is a part of the mathematical subject of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms on simplicial trees. The theory relates group actions on trees with decomposing groups as iterated applications of the operations of free product with amalgamation and HNN extension, via the notion of the fundamental group of a graph of groups. Bass–Serre theory can be regarded as one-dimensional version of the orbifold theory.

Attributes	Values
rdfs:label	Bass-Serre-Baum (de) Bass–Serre theory (en) Teoría de Bass-Serre (es)
rdfs:comment	Bass-Serre-Bäume sind eine Konstruktion aus dem mathematischen Teilgebiet der Gruppentheorie, mit der Gruppenwirkungen von amalgamierten Produkten oder allgemeiner Fundamentalgruppen von Graphen von Gruppen auf Bäumen konstruiert werden können. Sie sind nach Hyman Bass und Jean-Pierre Serre benannt. (de) Bass–Serre theory is a part of the mathematical subject of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms on simplicial trees. The theory relates group actions on trees with decomposing groups as iterated applications of the operations of free product with amalgamation and HNN extension, via the notion of the fundamental group of a graph of groups. Bass–Serre theory can be regarded as one-dimensional version of the orbifold theory. (en) En la teoría geométrica de grupos, la Teoría de Bass-Serre es una parte del tema matemático de la teoría de grupos y la topología combinatoria que trata del análisis de la estructura algebraica de las acciones de grupos, mediante automorfismos, sobre los árboles simpliciales. Esta teoría relaciona las acciones de los grupos sobre árboles con la descomposición de grupos como aplicaciones iteradas de las operaciones de producto libres con amalgamación y la de HNN-extensión, empleando principalmente el concepto de grupo fundamental de un grafo de grupos. (es)
dcterms:subject	Geometric group theory Group theory
Wikipage page ID	18673708 (xsd:integer)
Wikipage revision ID	1083562980 (xsd:integer)
Link from a Wikipage to another Wikipage	End (topology) Algebraic group Hyman Bass Index of a subgroup Kurosh subgroup theorem Lie group Geometric group theory Group theory Coset Mathematics Geometric group theory Geometric topology Real tree Quotient graph Eliyahu Rips Free product with amalgamation Geometrization conjecture Graph (discrete mathematics) Graph of groups Martin Dunwoody Fundamental group Haken manifold Deck transformation C. T. C. Wall Tree (graph theory) G. Peter Scott HNN extension Lattice (discrete subgroup) Local field Alexander Lubotzky Allen Hatcher 3-manifold Brian Bowditch Noetherian group Graph isomorphism Graph theory Kazhdan's property (T) Group action (mathematics) Group homomorphism Jean-Pierre Serre Covering space Abelian group Karen Vogtmann JSJ decomposition Teichmüller space Marc Culler Free abelian group Free group Free product Group isomorphism Group theory Groupoid Gromov-Hausdorff convergence Metric space Orbifold Kleinian group Rips machine Multiple edge Finitely generated group Finitely presented group Gilbert Baumslag Injective Ultralimit Universal covering space Bruhat–Tits building Word-hyperbolic group Group (math) Group presentation Spanning tree (mathematics) dbr:Complex_of_groups dbr:Graph_of_spaces dbr:Kac–Moody_group dbr:Limit_group
sameAs	Bass–Serre theory Bass–Serre theory Bass–Serre theory Bass–Serre theory Bass–Serre theory
dbp:wikiPageUsesTemplate	dbt:Overline dbt:Reflist
has abstract	Bass-Serre-Bäume sind eine Konstruktion aus dem mathematischen Teilgebiet der Gruppentheorie, mit der Gruppenwirkungen von amalgamierten Produkten oder allgemeiner Fundamentalgruppen von Graphen von Gruppen auf Bäumen konstruiert werden können. Sie sind nach Hyman Bass und Jean-Pierre Serre benannt. (de) Bass–Serre theory is a part of the mathematical subject of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms on simplicial trees. The theory relates group actions on trees with decomposing groups as iterated applications of the operations of free product with amalgamation and HNN extension, via the notion of the fundamental group of a graph of groups. Bass–Serre theory can be regarded as one-dimensional version of the orbifold theory. (en) En la teoría geométrica de grupos, la Teoría de Bass-Serre es una parte del tema matemático de la teoría de grupos y la topología combinatoria que trata del análisis de la estructura algebraica de las acciones de grupos, mediante automorfismos, sobre los árboles simpliciales. Esta teoría relaciona las acciones de los grupos sobre árboles con la descomposición de grupos como aplicaciones iteradas de las operaciones de producto libres con amalgamación y la de HNN-extensión, empleando principalmente el concepto de grupo fundamental de un grafo de grupos. La teoría de Bass-Serre puede ser considerada como la versión 1-dimensional de la teoría de orbidades y aporta un método muy importante cuando se estudia a los grupos infinitos discretos. (es)
gold:hypernym	Part
prov:wasDerivedFrom	wikipedia-en:Bass–Serre_theory?oldid=1083562980&ns=0
page length (characters) of wiki page	38859 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Bass–Serre_theory
is Link from a Wikipage to another Wikipage of	Buss-Serre covering tree Hyman Bass John R. Stallings

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software