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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 |
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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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