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fundamental concepts in differential geometry
The following is an index of fundamental concepts in differental geometry. It only deals with basic concepts which are common to all branches of differential geometry. For concepts pertinent to specific branches of differential geometry, please see concepts in symplectic geometry and concepts in Riemannian geometry
0.1 Manifolds

manifold with boundary

boundary manifold

coordinate map

coordinate neighborhood
0.2 Vector and Tensor Fields
0.3 Bundles and Connections

homotopic classification and characteristic classes

space of connections
0.4 Gauge theory
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