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《变换群与曲线模空间》是由高等教育出版社出版的。

内容简介

Transformation groups have played a fundamental role in many areas of mathematics such as differential geometry, geometric topology, algebraic topology, algebraic geometry, number theory. Ore of the basic reasons for their importance is that symmetries are described by groups (or rather group actions). Quotients of smooth manifolds by group actions are usually not smooth manifolds. On the other hand, if the actions of the groups are proper, then the quotients are orbifolds. An important example is given by the action of the mapping class groups on the Teichmuller spaces, and the quotients give the moduli spaces of Riemann surfaces (or algebraic curves) and are orbifolds.
This book consists of expanded lecture' notes of two summer schools Transformation Groups and Orbifolds and Geometry of Teichmuller Spaces and Moduli Spaces of Curves in 2008 and will be a valuable source for people to learn transformation groups, orbifolds, Teichmuller spaces, mapping class groups, moduli soaces of curves and related topics.

目录

Lectures on Orbifolds and Group Cohomology
Alejandro Adem and Michele Klaus
1 Introduction
2 Classical orbifolds
3 Examples of orbifolds
4 Orbifolds and manifolds
5 Orbifolds and groupoids
6 The orbifold Euler characteristic and K-theory
7 Stringy products in K-theory
8 Twisted version
References
Lectures on the Mapping Class Group of a Surface
Thomas Kwok-Keung Au, Feng Luo and Tian Yang
Introduction
1 Mapping class group
2 Dehn-Lickorish Theorem
3 Hyperbolic plane and hyperbolic surfaces
4 Quasi-isometry and large scale geometry
5 Dehn-Nielsen Theorem
References
Lectures on Orbifolds and Reflection Groups
Michael W. Davis
1 Transformation groups and orbifolds
2 2-dimensional orbifolds
3 Reflection groups
4 3-dimensional hyperbolic reflection groups
5 Aspherical orbifolds
References
Lectures on Moduli Spaces of Elliptic Curves
Richard Hain
1 Introduction to elliptic curves and the moduli problem
2 Families of elliptic curves and the universal curve
3 The orbifold M1,1
4 The orbifold ■1,1 and modular forms
5 Cubic curves and the universal curve ■→■1,1
6 The Picard groups of M1,1 and ■1,1
7 The algebraic topology of ■1,1
8 Concluding remarks
Appendix A Background on Riemann surfaces
Appendix B A very brief introduction to stacks
References
An Invitation to the Local Structures of Moduli of Genus One Stable Maps
Yi HU
1 Introduction
2 The structures of the direct image sheaf
3 Extensions of sections on the central fiber
References
Lectures on the ELSV Formula
Chiu-Chu Melissa Liu
1 Introduction
2 Hurwitz numbers and Hodge integrals
3 Equivariant cohomology and localization
4 Proof of the ELSV formula by virtual localization
References
Formulae of One-partition and Two-partition Hodge Integrals
Chiu-Chu Melissa Liu
1 Introduction
2 The Marino-Vafa formula of one-partition Hodge integrals
3 Applications of the Marifio-Vafa formula
4 Three approaches to the Marino-Vafa formula
5 Proof of Proposition 4.3
6 Generalization to the two-partition case
References
Lectures on Elements of Transformation Groups and Orbifolds
Zhi Lu
1 Topological groups and Lie groups
2 G-actions (or transformation groups) on topological spaces
3 Orbifolds
4 Homogeneous spaces and orbit types
5 Twisted product and slice
6 Equivariant cohomology
7 Davis-Januszkiewicz theory
References
The Action of the Mapping Class Group on Representation Varieties
Richard A. Wentworth
1 Introduction
2 Action of Out (π) on representation varieties
3 Action on the cohomology of the space of fiat unitary connections
4 Action on the cohomology of the SL (2, C) character variety
References

前言/序言

Transformation groups have played a fundamental role in many areas of mathematics such as differential geometry, geometric topology, algebraic topology, algebraic geometry, number theory. One of the basic reasons for their importance is that symmetries are described by groups (or rather group actions). Indeed, the existence of group actions makes the spaces under study more interesting, and properties of groups can also be understood better by studying their actions on suitable spaces.
Quotients of smooth manifolds by group actions are usually not smooth manifolds. On the other hand, if the actions of the groups are proper, then the quotients are orbifolds.
The notion of V-manifolds was first introduced by Satake in 1956 in the con-text of locally symmetric spaces and automorphic forms. V-manifolds were reintroduced and renamed orbifolds by Thurston near the end of 1978 in connection with the Thurston geometrization conjecture on the geometry of three dimensional manifolds. Basically, orbifolds are locally quotients of smooth manifolds by finite groups. Besides arising from transformation groups, many natural spaces in number theory and algebraic geometry are orbifolds.
变换群与曲线模空间（英文版） [Transformation Groups and Moduli Spaces of Curves] 电子书 下载 mobi epub pdf txt

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京东5折促销买的，很实惠。

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先说外观 不错 包装很好装订的也不错 字体大小适中 感觉很舒服 内容 很博大 涉及很多很多 真的是对一个人知识面理解力的考验 要细细的读 不断的品 现在还没读完 但是 依然推荐

评分☆☆☆☆☆

先说外观 不错 包装很好装订的也不错 字体大小适中 感觉很舒服 内容 很博大 涉及很多很多 真的是对一个人知识面理解力的考验 要细细的读 不断的品 现在还没读完 但是 依然推荐

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