- 量化辛几何导引(英文版数学研究生系列教材)
- - 作者：编者:张俊//祝安铜|责编:韩继伟
  - 出版社：中国科大
  - ISBN：9787312062827
  - 出版日期：2025/06/01
  - 页数：364
- 售价：32

内容大纲
本书系统介绍辛几何与切触几何的核心理论与前沿进展。内容涵盖基础理论、Moser技巧、哈密尔顿Floer理论和辛同调等；聚焦量子上同调、拉格朗日配边和微局部层论，以代数方法替代传统Floer理论；突出定量工具（如持续同调、形不变量等）在刚性研究中的应用；高效证明Arnold不动点猜想、Gromov不可压缩定理等经典结论。
本书兼顾理论推导与计算实践，每章配备大量例题，既适合入门教学，也可为研究者提供前沿参考。
作者介绍
目录
Preface
Chapter 1 Symplectic Manifold
  1.1  Symplectic Structure
  1.2  Examples of Symplectic Manifolds
  1.3  Almost Complex Structure
  1.4  J-Holomorphic Curve (Part One)
  1.5  Symplectomorphism
  1.6  Lagrangian Submanifold
  1.7  Hamiltonian Diffeomorphism
Chapter 2 Physics in Symplectic Topology
  2.1  Lagrangian Mechanics
  2.2  Hamiltonian Mechanics
  2.3  Poisson Bracket
  2.4  Group Action
  2.5  Moment Map
  2.6  Integrable System
  2.7  Noether's Principle
  2.8  Local Description
Chapter 3 Contact Geometry
  3.1  Contact Structure
  3.2  Contact Manifold
  3.3  J-Holomorphic Curve (Part Two)
  3.4  Legendrian Submanifolds
  3.5  Contact Hamiltonian Dynamics
  3.6  Contact Poisson Bracket
  3.7  Orderability
Chapter 4 Moser's Argument
  4.1  Moser's Trick
  4.2  Stability Theorems
  4.3  Neighborhood Theorems
Chapter 5 Floer Theory
  5.1  Morse Theory
  5.2  Persistence Module
  5.3  Homological Rigidity
  5.4  ∞-dimensional Morse Theory
  5.5  Indices
Chapter 6 Quantitative Characterizations
  6.1  Hofer's Geometry
  6.2  Chaotic Hamiltonian Dynamics
  6.3  Symplectic Homology
  6.4  Symplectic Capacity
Chapter 7 Miscellaneous
  7.1  Floer Continuation Map
  7.2  Toric Domains
  7.3  Shape Invariant
Chapter 8 Quantum Cohomology
  8.1  Novikov Field (Ring)
  8.2  Non-Archimedean Linear Algebra
  8.3  Stable Map
  8.4  Quantum Cohomology Group

  8.5  Gromov-Witten Invariant
  8.6  Gromov-Witten Potential
  8.7  Back to Quantum Cohomology
Chapter 9 Hard Stories on Lagrangians
  9.1  More Examples
  9.2  A∞-algebra and Potential Function
  9.3  Distance Between Lagrangians (Small Scale)
  9.4  Distance Between Lagrangians (Large Scale)
  9.5  Lagrangian Cobordism
  9.6  Triangulated Category
  9.7  Neck-Stretching
Chapter 10 A Different Language—Sheaf
  10.1  Generating Function
  10.2  A Crash Course on Sheaf
  10.3  Sheaf Cohomology
  10.4  Derived Category and Derived Functor
  10.5  i-th Derived Functor And Its Computation
  10.6  Singular Support (I)
  10.7  Singular Support (II)
  10.8  Arnold-Givental's Conjecture
Appendix Exams
  I Midterm Exam (MATH6435P - USTC, Spring 2023)
  II Final Exam (MATH6435P - USTC, Spring 2023)
  III Midterm Exam (MATH6437P - USTC, Spring 2024)
  IV Final Exam (MATH6437P - USTC, Spring 2024)
Bibliography
Index

内容大纲

作者介绍

目录

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