Abstract differential geometry is a branch of mathematics that studies geometric structures on manifolds in a more general and abstract setting, primarily using concepts from differential geometry and algebraic topology. It emphasizes the intrinsic properties of geometric objects without necessarily attributing them to any specific coordinate system or representation. Some key features of abstract differential geometry include: 1. **Smooth Manifolds**: Abstract differential geometry focuses on smooth manifolds, which are spaces that locally resemble Euclidean space and possess a differentiable structure.
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