Hilbert's fifth problem and related topics / Terence Tao

Auteur: Tao, Terence (1975-) - AuteurType de document: MonographieCollection: Graduate studies in mathematics ; 153Langue: anglaisPays: Etats UnisÉditeur: Providence : American Mathematical Society, 2014Description: 1 vol. (XIII-338 p.) ; 27 cm ISBN: 9781470415648 ; rel. Note: Hilbert’s fifth problem asks about a topological description of Lie groups without any direct reference to smooth structures. This question can be formalized in a number of ways but one of a commonly accepted formulation asks whether any locally Euclidean topological group is necessarily a Lie group. This question was answered affirmatively by Gleason and by Montgomery and Zippin. The book focuses on three related topics: (a) Topological description of Lie groups and the classification of locally compact groups, (b) approximate groups in nonabelian groups and their classification via the Gleason-Yamabe theorem, and (c) Gromov’s theorem on finitely generated groups of polynomial growth and consequences to fundamental groups of Riemannian manifolds. ... (Zentralblatt)Bibliographie: Bibliogr. p. 329-333. Index. Sujets MSC: 22D05 Topological groups, Lie groups -- Locally compact groups and their algebras -- General properties and structure of locally compact groups
22E05 Topological groups, Lie groups -- Lie groups -- Local Lie groups
22E15 Topological groups, Lie groups -- Lie groups -- General properties and structure of real Lie groups
22-02 Topological groups, Lie groups -- Research exposition (monographs, survey articles)
20F65 Group theory and generalizations -- Special aspects of infinite or finite groups -- Geometric group theory
En-ligne: Zentralblatt
Location Call Number Status Date Due
Salle R 12366-01 / 22 TAO (Browse Shelf) Available

Hilbert’s fifth problem asks about a topological description of Lie groups without any direct reference to smooth structures. This question can be formalized in a number of ways but one of a commonly accepted formulation asks whether any locally Euclidean topological group is necessarily a Lie group. This question was answered affirmatively by Gleason and by Montgomery and Zippin. The book focuses on three related topics: (a) Topological description of Lie groups and the classification of locally compact groups, (b) approximate groups in nonabelian groups and their classification via the Gleason-Yamabe theorem, and (c) Gromov’s theorem on finitely generated groups of polynomial growth and consequences to fundamental groups of Riemannian manifolds. ... (Zentralblatt)

Bibliogr. p. 329-333. Index

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