Differential topology is an area of mathematics that deals with the properties of geometric objects like surfaces and curves. Synonyms for differential topology include differential geometry, which focuses on using calculus to study geometric objects, and algebraic topology, which studies shapes and spaces by using algebraic tools. Other synonyms include differential equations, topological spaces, manifolds, and fiber bundles. These fields are interconnected and often rely on each other to solve complex problems. Differential topology is used in a variety of applications, including physics, engineering, and computer science. It is a fascinating area of study for mathematicians and scientists who are interested in the properties of geometrical objects and their underlying structures.