Differential topology is a branch of mathematics that focuses on the study of differentiable functions on differentiable manifolds. It explores how smooth structures can be understood in terms of their geometric and topological properties, making it vital for analyzing the shapes and behaviors of objects in higher dimensions. This field bridges concepts from calculus and topology, helping to understand how small changes in input can affect the overall structure, which is essential when discussing the implications of critical points and isomorphisms.
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