Geometry of Low-Dimensional Manifolds(London Mathematical Society Lecture Note Series)

基本信息

Edited by:S.K. Donaldson, C.B. Thomas

Series:London Mathematical Society Lecture Note Series

Format:Paperback / softback 260 pages

Publisher:Cambridge University Press

Imprint:Cambridge University Press

ISBN:9780521400015

Published:24 Jan 1991

Weight:319g

Dimensions:152 x 230 x 17 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

本卷是基于在低维流形几何的杜伦LMS研讨会上的讲座课程和研讨会。这一领域是最近研究的热点之一，其重大突破阐明了许多不同学科相互作用的方式(例如:拓扑、微分和代数几何以及数学物理)。研讨会邀请了一些杰出人士就这些问题举办讲座和研讨会；已经有结果的卷书是许多材料的w一说明性的来源，并且对于所有几何和数学物理研究工作者来说是必不可少的。。

This volume is based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds. This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects interact (for example: topology, differential and algebraic geometry and mathematical physics). The workshop brought together a number of distinguished figures to give lecture courses and seminars in these subjects; the volume that has resulted is the only expository source for much of the material, and will be essential for all research workers in geometry and mathematical physics.

目录

Names of Participants

Introduction

Acknowledgements

Part I. Symplectic Geometry:

1. Introduction

2. Rational and ruled symplectic 4-manifolds Dusa McDuff

3. Symplectic capacities H. Hofer

4. The nonlinear Maslov index A. B. Givental

5. Filling by holomorphic discs and its applications Yakov Eliashberg

Part II. Jones/Witten Theory:

6. Introduction

7. New results in Chern-Simons theory Edward Witten, notes by Lisa Jeffrey

8. Geometric quantization of spaces of connections N. J. Hitchin

9. Evaluations of the 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C) Robion Kirby and Paul Melvin

10. Representations of braid groups M. F. Atiyah, notes by S. K. Donaldson

Part III. Three-Dimensional Manifolds:

11. Introduction

12. An introduction to polyhedral metrics of non-positive curvature on 3-manifolds I. R. Aitchison and J. H. Rubinstein

13. Finite groups of hyperbolic isometries C. B. Thomas

14. Pin structures on low-dimensional manifolds R. C. Kirby and L. R. Taylor.

作者简介

西蒙·唐纳森（Donaldson，Simon，1957年8月—）英国数学家。1986年于伯克利获菲尔茨奖。获奖时在牛津大学任职。

关于四维流形拓扑的研究。他发现了四维几何学中难以预料与神秘的现象，得出存在“怪异”四维空间的结论，即与标准欧氏空间R1拓扑同胚但不微分同胚的微分流形。

Sir Simon Kirwan Donaldson FRS (born 20 August 1957) is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds and Donaldson–Thomas theory. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London.

C. B. Thomas