Elliptic Operators, Topology and Asymptotic Methods
Elliptic Operators, Topology and Asymptotic Methods
复制标题
椭圆算子、拓扑和渐近方法
DOI：
10.1201/b16418
复制
发表时间：
1988
影响因子：
2.5
通讯作者：
J. Roe
中科院分区：
文献类型：
--
作者：
J. Roe
黎曼几何连接的简历黎曼几何微分形式练习连接，曲率，和特征类主丛及其联系特征类一般笔记练习Clifford代数和Dirac算子Clifford丛和Dirac算子Clifford丛和Clifford丛的曲率例子笔记练习自旋群Clifford代数作为Clifford代数表示中的可逆超代数群Clifford代数理论流形上的自旋结构自旋丛和特征类复自旋群笔记练习Dirac算子的分析性质Sobolev空间Dirac算子的分析泛函微积分笔记练习霍奇理论笔记练习热和波动存在方程和唯一性定理热核的渐近展开波动方程的有限传播速度笔记练习迹线和本征值渐近本征值增长迹类算子Weyl的渐近公式笔记练习一些非紧流形的调和振子维滕的扰动de Rham复泛函微积分在开流形上的笔记练习莱夫谢茨公式莱夫谢茨数固定-分数贡献笔记练习指数问题分次和Clifford Bundles分次Dirac算子热方程和指数定理笔记练习Getzler微积分和局部指标定理过滤代数和符号Getzler符号热核的Getzler符号精确解指标定理笔记练习指标定理的应用旋量Dirac算子签名定理Hirzebruch-Riemann-Roch定理局部指标理论笔记练习维滕对莫尔斯理论的方法莫尔斯不等式莫尔斯函数圆点的贡献笔记Atiyah的-指数定理光滑算子代数重整维数与指数定理注记
Resume of Riemannian Geometry Connections Riemannian Geometry Differential Forms Exercises Connection, Curvature, and Characteristic Classes Principal Bundles and their Connections Characteristic Classes Genera Notes Exercises Clifford Algebras and Dirac Operators Clifford Bundles and Dirac Operators Clifford Bundles and Curvature Examples of Clifford Bundles Notes Exercises The Spin Groups The Clifford Algebra as a Superalgebra Groups of Invertibles in the Clifford Algebra Representation Theory of the Clifford Algebra Spin Structures on Manifolds Spin Bundles and Characteristic Classes The Complex Spin Group Notes Exercises Analytic Properties of Dirac Operators Sobolev Spaces Analysis of the Dirac Operator The Functional Calculus Notes Exercises Hodge Theory Notes Exercises The Heat and Wave Equations Existence and Uniqueness Theorems The Asymptotic Expansion for the Heat Kernel Finite Propagation Speed for the Wave Equation Notes Exercises Traces and Eigenvalue Asymptotics Eigenvalue Growth Trace-Class Operators Weyl's Asymptotic Formula Notes Exercises Some Non-Compact Manifolds The Harmonic Oscillator Witten's Perturbation of the de Rham Complex Functional Calculus on Open Manifolds Notes Exercises The Lefschetz Formula Lefschetz Numbers The Fixed-Point Contributions Notes Exercises The Index Problem Gradings and Clifford Bundles Graded Dirac Operators The Heat Equations and the Index Theorem Notes Exercises The Getzler Calculus and the Local Index Theorem Filtered Algebras and Symbols Getzler Symbols The Getzler Symbol of the Heat Kernel The Exact Solution The Index Theorem Notes Exercises Applications of the Index Theorem The Spinor Dirac Operator The Signature Theorem The Hirzebruch-Riemann-Roch Theorem Local Index Theory Notes Exercises Witten's Approach to Morse Theory The Morse Inequalities Morse Functions The Contribution from the Circle Points Notes Atiyah's -Index Theorem An Algebra of Smoothing Operators Renormalized Dimensions an the Index Theorem Notes References