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Hilbert第五问题及相关论题（影印版）

样章
作者：
Terence Tao
定价：
169.00元
ISBN：
978-7-04-055629-2
版面字数：
580.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2021-03-09
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
数论
暂无
  • 前辅文
  • 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
    • Chapter 8. Models of ultra approximate groups
      • §8.1. Ultralimits of metric spaces (Optional)
      • §8.2. Sanders-Croot-Sisask theory
      • §8.3. Locally compact models of ultra approximate groups
      • §8.4. Lie models of ultra approximate groups
    • Chapter 9. The microscopic structure of approximate groups
      • §9.1. Gleason's lemma
      • §9.2. A cheap version of the structure theorem
      • §9.3. Local groups
    • Chapter 10. Applications of the structural theory of approximate groups
      • §10.1. Sets of bounded doubling
      • §10.2. Polynomial growth
      • §10.3. Fundamental groups of compact manifolds (optional)
      • §10.4. A Margulis-type lemma
  • Part 2. Related Articles
    • Chapter 11. The Jordan-Schur theorem
      • §11.1. Proofs
    • Chapter 12. Nilpotent groups and nilprogressions
      • §12.1. Some elementary group theory
      • §12.2. Nilprogressions
    • Chapter 13. Ado's theorem
      • §13.1. The nilpotent case
      • §13.2. The solvable case
      • §13.3. The general case
    • Chapter 14. Associativity of the Baker-Campbell-Hausdorff-Dynkin law
    • Chapter 15. Local groups
      • §15.1. Lie's third theorem
      • §15.2. Globalising a local group
      • §15.3. A nonglobalisable group
    • Chapter 16. Central extensions of Lie groups, and cocycle averaging
      • §16.1. A little group cohomology
      • §16.2. Proof of theorem
    • Chapter 17. The Hilbert-Smith conjecture
      • §17.1. Periodic actions of prime order
      • §17.2. Reduction to the p-adic case
    • Chapter 18. The Peter-Weyl theorem and nonabelian Fourier analysis
      • §18.1. Proof of the Peter-Weyl theorem
      • §18.2. Nonabelian Fourier analysis
    • Chapter 19. Polynomial bounds via nonstandard analysis
    • Chapter 20. Loeb measure and the triangle removal lemma
      • §20.1. Loeb measure
      • §20.2. The triangle removal lemma
    • Chapter 21. Two notes on Lie groups
  • Bibliography
  • Index

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