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- Fundamental_group abstract "In mathematics, more specifically algebraic topology, the fundamental group (defined by Henri Poincaré in his article Analysis Situs, published in 1895) is a group associated to any given pointed topological space that provides a way of determining when two paths, starting and ending at a fixed base point, can be continuously deformed into each other. Intuitively, it records information about the basic shape, or holes, of the topological space. The fundamental group is the first and simplest of the homotopy groups. It is a topological invariant: homeomorphic topological spaces have the same fundamental group.Fundamental groups can be studied using the theory of covering spaces, since a fundamental group coincides with the group of deck transformations of the associated universal covering space. The abelianisation of the fundamental group can be identified with the first homology group of the space. When the topological space is homeomorphic to a simplicial complex, its fundamental group can be described explicitly in terms of generators and relations.Historically, the concept of fundamental group first emerged in the theory of Riemann surfaces, in the work of Bernhard Riemann, Henri Poincaré and Felix Klein, where it describes the monodromy properties of complex functions, as well as providing a complete topological classification of closed surfaces.".
- Fundamental_group wikiPageExternalLink topo_alg.
- Fundamental_group wikiPageExternalLink ATpage.html.
- Fundamental_group wikiPageExternalLink VIGREREU2008.html.
- Fundamental_group wikiPageID "11004".
- Fundamental_group wikiPageRevisionID "603585156".
- Fundamental_group hasPhotoCollection Fundamental_group.
- Fundamental_group id "3941".
- Fundamental_group id "849".
- Fundamental_group title "Fundamental group".
- Fundamental_group title "Fundamental groupoid".
- Fundamental_group urlname "FundamentalGroup".
- Fundamental_group subject Category:Algebraic_topology.
- Fundamental_group subject Category:Homotopy_theory.
- Fundamental_group comment "In mathematics, more specifically algebraic topology, the fundamental group (defined by Henri Poincaré in his article Analysis Situs, published in 1895) is a group associated to any given pointed topological space that provides a way of determining when two paths, starting and ending at a fixed base point, can be continuously deformed into each other. Intuitively, it records information about the basic shape, or holes, of the topological space.".
- Fundamental_group label "Fundamentaalgroep".
- Fundamental_group label "Fundamental group".
- Fundamental_group label "Fundamentalgruppe".
- Fundamental_group label "Groupe fondamental".
- Fundamental_group label "Grupa podstawowa".
- Fundamental_group label "Grupo fundamental".
- Fundamental_group label "Grupo fundamental".
- Fundamental_group label "Gruppo fondamentale".
- Fundamental_group label "Фундаментальная группа".
- Fundamental_group label "زمرة أساسية".
- Fundamental_group label "基本群".
- Fundamental_group label "基本群".
- Fundamental_group sameAs Fundamentální_grupa.
- Fundamental_group sameAs Fundamentalgruppe.
- Fundamental_group sameAs Grupo_fundamental.
- Fundamental_group sameAs Groupe_fondamental.
- Fundamental_group sameAs Gruppo_fondamentale.
- Fundamental_group sameAs 基本群.
- Fundamental_group sameAs 기본군.
- Fundamental_group sameAs Fundamentaalgroep.
- Fundamental_group sameAs Grupa_podstawowa.
- Fundamental_group sameAs Grupo_fundamental.
- Fundamental_group sameAs m.02z4l.
- Fundamental_group sameAs Q662830.
- Fundamental_group sameAs Q662830.
- Fundamental_group wasDerivedFrom Fundamental_group?oldid=603585156.
- Fundamental_group isPrimaryTopicOf Fundamental_group.