Part I: Geometries and General Group Actions

Handbook of Group Actions（群作用手册）（第 I 卷）作者：季理真, Papadopoulos, 丘成桐　　 ISBN：978-7-04-041363-2　出版时间：2014-12-25

内封

版权

目录

前辅文

Part I: Geometries and General Group Actions

Geometry of Singular Space

Shing-Tung Yau

References

A Summary of Topics Related to Group Actions

Lizhen Ji

References

Part II: Mapping Class Groups and Teichm¨uller Spaces Actions of Mapping Class Groups

Athanase Papadopoulos

References

The Mapping Class Group Action on the Horofunction Compactification of Teichm¨uller Space

Weixu Su

References

Schottky Space and Teichm¨uller Disks

Frank Herrlich

References

Topological Characterization of the Asymptotically Trivial Mapping Class Group

Ege Fujikawa

References

The Universal Teichm¨uller Space and Diffeomorphisms of the Circle with H¨older Continuous Derivatives

Katsuhiko Matsuzaki

References

On the Johnson Homomorphisms of the Mapping Class Groups of urfaces

References

Part III: Hyperbolic Manifolds and Locally Symmetric Spaces The Geometry and Arithmetic of Kleinian Groups

Gaven JMartin

References

Weakly Commensurable Groups, with Applications to Differential Geometry

Gopal Prasad and Andrei SRapinchuk

References

Part IV: Knot Groups

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

Takayuki Morifuji

References

Meridional and Non-meridional Epimorphisms between Knot Groups

Masaaki Suzuki

References
- Geometry of Singular Space
- Shing-Tung Yau
- 1 The development of modern geometry that influenced ourconcept of space
- 2 Geometry of singular spaces
- 3 Geometry for Einstein equation and special holonomy group
- 4 The Laplacian and the construction of generalized Riemanniangeometry 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-Millstheory
- 8 Generalized manifolds with special holonomy groups
- 9 Maps, subspaces and sigmamodels
- 10 Noncompactmanifolds
- 11 Discrete spaces
- 12 Conclusion
- 13 Appendix
- References
- A Summary of Topics Related to Group Actions
- Lizhen Ji
- 1 Introduction
- 2 Different types of groups
- 3 Different types of group actions
- 4 How do group actions arise
- 5 Spaces which support group actions
- 6 Compact transformation groups
- 7 Noncompact transformation groups
- 8 Quotient spaces of discrete group actions
- 9 Quotient spaces of Lie groups and algebraic group actions
- 10 Understanding groups via actions
- 11 How to make use of symmetry
- 12 Understanding and classifying nonlinear actions of groups
- 13 Applications of finite group actions in combinatorics
- 14 Applications in logic
- 15 Groups and group actions in algebra
- 16 Applications in analysis
- 17 Applications in probability
- 18 Applications in number theory
- 19 Applications in algebraic geometry
- 20 Applications in differential geometry
- 21 Applications in topology
- 22 Group actions and symmetry in physics
- 23 Group actions and symmetry in chemistry
- 24 Symmetry in biology and the medical sciences
- 25 Group actions and symmetry in material science and engineering
- 26 Symmetry in arts and architecture
- 27 Group actions and symmetry in music
- 28 Symmetries in chaos and fractals
- 29 Acknowledgements and references
- References

Book Metrics 引用导出

点击：次

下载：次