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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra Cohomology Theories for Compact Abelian Groups
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Cohomology Theories for Compact Abelian Groups
Karl H. Hofmann, Paul S. Mostert (Broschiert, Englisch)
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Beschreibung
Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used… in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of com pact abelian groups. An added element of elegance is the duality theory, which states that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact. groups as it may seem at first glance. As is very well known, the local geometric structure of a compact group may be extremely complicated, but all local complication happens to be "abelian". Indeed, via the duality theory, the complication in compact connected groups is faithfully reflected in the theory of torsion free discrete abelian groups whose notorious complexity has resisted all efforts of complete classification in ranks greater than two. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
14.12.2011
Sprache
Englisch
EAN
9783642806728
Herausgeber
Springer Berlin
Sonderedition
Nein
Autor
Karl H. Hofmann, Paul S. Mostert
Seitenanzahl
236
Auflage
1973
Einbandart
Broschiert
Schlagwörter
Abelian group, Algebraic structure, Cohomology, Group theory, Representation theory
Thema-Inhalt
PBG - Gruppen und Gruppentheorie
Höhe
244 mm
Breite
17 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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