内容

目次

Elements of Differential Calculus from an Algebraic Viewpoint: AlgebraicTools; Smooth Manifolds; Vector Bundles; Vector Fields; Differential Forms;Lie Derivative; Basic Differential Calculus on Fat Manifolds: BasicDefinitions; The Lie Algebra of Der-operators; Fat Vector Fields; Fat Fieldsand Vector Fields on the Total Space; Induced Der-operators; FatTrajectories; Inner Structures; Linear Connections: Basic Definitions andExamples; Parallel Translation; Curvature; Operations with LinearConnections; Linear Connections and Inner Structures; Covariant Differential:Fat de Rham Complexes; Covariant Differential; Compatible Linear Connections;Linear Connections Along Fat Maps; Covariant Lie Derivative; CohomologicalAspects of Linear Connections: An Introductory Example; Cohomology of FlatLinear Connections; Homotopy Formula for Linear Connections.