Preface Notation Acknowledgments Part 1． Hilbert's Fifth Problem Chapter 1． Introduction §1．1． Hilbert's fifth problem §1．2． Approximate groups §1．3． Gromov's theorem Chapter 2． Lie groups， Lie algebras， and the Baker-Campbell-Hausdorff formula §2．1． Local groups §2．2． Some differential geometry §2．3． The Lie algebra of a Lie group §2．4． The exponential map §2．5． The Baker-Campbell-Hausdorff formula Chapter 3． Building Lie structure from representations and metrics §3．1． The theorems of Cartan and von Neumann §3．2． Locally compact vector spaces §3．3． From Gleason metrics to Lie groups Chapter 4． Haar measure， the Peter-Weyl theorem． and compact or abelian groups §4．1． Haar measure §4．2． The Peter-Weyl theorem §4．3． The structure of locally compact abelian groups Chapter 5． Building metrics on groups， and the Gleason-Yamabe theorem §5．1． Warmup： the Birkhoff-Kakutani theorem §5．2． Obtaining the commutator estimate via convolution §5．3． Building metrics on NSS groups §5．4． NSS from subgroup trapping §5．5． The subgroup trapping property §5．6． The local group case Chapter 6．The structure of locally compact groups §6．1． Van Dantzig's theorem §6．2． The invariance of domain theorem §6．3． Hilbert's fifth problem §6．4． Transitive actions Chapter 7． Ultraproducts as a bridge between hard analysis and soft analysis §7．1． Ultrafilters §7．2． Ultrapowers and ultralimits §7．3． Nonstandard finite sets and nonstandard finite sums §7．4． Asymptotic notation §7．5． Ultra approximate groups …… Part 2． Related Articles Bibliography Index
鄂公網(wǎng)安備 42010302001612號(hào) 