What is d maps?

D maps, or differential maps, are a mathematical concept used in differential geometry and topology to describe how smooth functions transform geometric structures such as manifolds and vector fields.

A differential map is a function that preserves the smoothness of the original structures, meaning that it produces a new structure that is also smooth and well-behaved. These maps are commonly used in modeling various phenomena in physics, engineering, and other sciences where the relationships between different mathematical objects need to be analyzed.

Differential maps are often expressed using the language of calculus and involve derivatives, Jacobian matrices, and other mathematical tools for analyzing the behavior of smooth functions. They are a fundamental concept in modern geometry and topology and have many applications in fields like robotics, computer graphics, and image processing.