群作用手册(第1卷) 高等教育出版社 mobi 下载 网盘 caj lrf pdf txt 阿里云

群和群作用是数学研究的重要对象，拥有强大的力量并且富于美感，这可以通过它广泛出现在诸多不同的科学领域体现出来。此多卷本手册由相关领域专家撰写的一系列综述文章组成，首次系统地展现了群作用及其应用，内容囊括经典主题的讨论、近来的热点专业问题的论述，有些文章还涉及相关的历史。《群作用手册（第1卷）》填补了数学著作中的一项空白，适合于从初学者到相关领域专家的各个层次读者阅读。

Part Ⅰ:Geometries and General Group Acti***

Geometry of Singular Space Shing-Tung Yau

1 The development of modern geometry that influenced our concept of space

2 Geometry of singular spaces

3 Geometry for Einstein equation and special holonomy group

4 The Laplacian and the c***truction of generalized Riemannian geometry in terms of operators

5 Differential topology of the operator geometry

6 Inner product on tangent spaces and Hodge theory

7 Gauge groups,convergence of operator manifolds and Yang-Mills theory

8 Generalized manifolds with special holonomy groups

9 Maps,subspaces and sigma models

10 Noncompact manifolds

11 Discrete spaces

12 Conclusion

13 Appendix

References

A Summary of Topics Related to Group Acti***

Lizhen Ji

1 Introduction

2 Different types of groups

3 Different types of group acti***

4 How do group acti*** arise

5 Spaces which *** group acti***

6 Compact transformation groups

7 Noncompact transformation groups

8 Quotient spaces of discrete group acti***

9 Quotient spaces of Lie groups and algebraic group acti***

I0 Understanding groups via acti***

11 How to make use of symmetry

12 Understanding and classifying nonlinear acti*** of groups

13 Applicati*** of finite group acti*** in combinatorics

14 Applicati*** in logic

15 Groups and group acti*** in algebra

16 Applicati*** in ***ysis

17 Applicati*** in probability

18 Applicati*** in number theory

19 Applicati*** in algebraic geometry

20 Applicati*** in differential geometry

21 Applicati*** in topology

22 Group acti*** and symmetry in physics

23 Group acti*** and symmetry in chemistry

24 Symmetry in biology and the medical sciences

25 Group acti*** and symmetry in material science and engineering

26 Symmetry in arts and architecture

27 Group acti*** and symmetry in music

28 Symmetries in chaos and fractals

29 Acknowledgements and references

References

Part Ⅱ:Mapping Class Groups and Teichmiiller Spaces

Acti*** of Mapping Class Groups

Athanase Papadopoulos

1 Introduction

2 Rigidity and acti*** of mapping class groups

3 Acti*** on foliati*** and laminati***

4 Some perspectives

References

The Mapping Class Group Action on the Horofunction Compactification of Teichmiiller Space

Weixu Su

1 Introduction

2 Background

3 Thurston's compactification of Teichmiiller space

4 Compactification of Teichmfiller space by extremal length

5 Analogies between the Thurston metric and the Teichmiiller metric

6 Detour cost and Busemann points

7 The extended mapping class group as an isometry group

8 On the classification of mapping class acti*** on Thurston's metric

9 Some questi***

References

Sc***tky Space and Teichmiiller Disks

Frank Herrlich

1 Introduction

2 Sc***tky coverings

3 Sc***tky space

4 Sc***tky and Teichmfiller space

5 Sc***tky space as a moduli space

6 Teichmiiller disks

7 Veech groups

8 Horizontal cut systems

9 Teichmiiller disks in Sc***tky space

References

Topological Characterization of the Asymptotically Trivial Mapping Class Group

Ege Fujikawa

1 Introduction

2 Preliminaries

3 Discontinuity of the Teichmfiller modular group action

4 The intermediate Teichmiiller space

5 Dynamics of the Teichmiiller modular group

6 A fixed point theorem for the asymptotic Teichmiiller modular group

7 Periodicity of asymptotically Teichmiiller modular transformation

References

The Universal Teichmiiller Space and Diffeomorphisms of the Circle with HSlder Continuous Derivatives

Katsuhiko Matsuzaki

1 Introduction

2 Quasisymmetric automorphisms of the circle

3 The universal Teichmiiller space

4 Quasisymmetric functi*** on the real line

5 Symmetric automorphisms and functi***

6 The small subspace

7 Diffeomorphisms of the circle with HSlder continuous derivatives

8 The Teichmiiller space of circle diffeomorphisms

References

On the Johnson Homomorphisms of the Mapping Class Groups of Surfaces

Ta*** Satoh

1 Introduction

2 Notation and conventi***

3 Mapping class groups of surfaces

4 Johnson homomorphisms of Aut Fn

5 Johnson homomorphisms of A4g,1

6 Some other applicati*** of the Johnson homomorphisms

Acknowledgements

References

Part Ⅲ:Hyperbolic Manifolds and Locally Symmetric Spaces

The Geometry and Arithmetic of Kleinian Groups

Gaven J.Martin

1 Introduction

2 The volumes of hyperbolic orbifolds

3 The Margulis c***tant for Kleinian groups

4 The general theory

5 Basic concepts

6 Two-generator groups

7 Polynomial trace identities and inequalities

8 Arithmetic hyperbolic geometry

9 Spaces of discrete groups,p,q E {3,4,5}

10 (p,q,r)-Kleinian groups

References

Weakly Commensurable Groups,with Applicati*** to Differential Geometry

Gopal Prasad and Andrei S.Rapinchuk

1 Introduction

2 Weakly commensurable Zariski-dense subgroups

3 Results on weak commensurability of S-arithmetic groups

4 Absolutely almost *** algebraic groups having the same maximal tori

5 A finiteness result

6 Back to geometry

Acknowledgements

References

Part Ⅳ:Knot Groups

Representati*** of Knot Groups into SL(2,C) and Twisted Alexander Polynomials

Takayuki Morifuji

1 Introduction

2 Alexander polynomials

3 Representati*** of knot groups into SL(2,C)

4 Deformati*** of representati*** of knot groups

5 Twisted Alexander polynomials

6 Twisted Alexander polynomials of hyperbolic knots

Acknowledgements

References

Meridional and Non-meridional Epimorphisms between Knot Groups

Masaaki Suzuki

1 Introduction

2 Some relati*** on the set of knots

3 Twisted Alexander polynomial and epimorphism

4 Meridional epimorphisms

5 Non-meridional epimorphisms

6 The relation≥on the set of prime knots

7 Simon's conjecture and other problems

Acknowledgements

References

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群和群作用是数学研究的重要对象，拥有强大的力量并且富于美感，这可以通过它广泛出现在诸多不同的科学领域体现出来。

此多卷本手册由相关领域专家撰写的一系列综述文章组成，首次系统地展现了群作用及其应用，内容囊括经典主题的讨论、近来的热点专业问题的论述，有些文章还涉及相关的历史。《群作用手册（第1卷）》填补了数学著作中的一项空白，适合于从初学者到相关领域专家的各个层次读者阅读。