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Differential Geometry

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Author(s): J. A. Ross, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part III Lecture Notes
Publisher: University of Cambridge
Year: 2016

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; geometry; topology; algebra; abstract algebra; modern algebra

Introduction
Manifolds
Manifolds
Smooth functions and derivatives
Bump functions and partitions of unity
Submanifolds
Vector fields
The tangent bundle
Flows
Lie derivative
Lie groups
Vector bundles
Tensors
Vector bundles
Differential forms and de Rham cohomology
Differential forms
De Rham cohomology
Homological algebra and Mayer-Vietoris theorem
Integration
Orientation
Integration
Stokes Theorem
De Rham's theorem*
Connections
Basic properties of connections
Geodesics and parallel transport
Riemannian connections
Curvature
Index