Differential Topology

Differential topology is a branch of mathematics that studies the properties of shapes and spaces that are smooth, meaning they have no sharp edges or corners. It combines aspects of both differential geometry and topology, focusing on how smooth, differentiable structures can be understood and transformed without tearing or gluing. Differential topologists explore concepts like curves, surfaces, and higher-dimensional manifolds, examining how they can bend and stretch while preserving their essential characteristics. This field has applications in physics, robotics, and computer graphics, where understanding smooth shapes and their transformations is crucial.