👉 In mathematics, a manifold is an abstract concept that describes a space that can be put into one-to-one correspondence with Euclidean space. It is a mathematical object which can be described in terms of its topological properties and geometric structure. A manifold is named after the study of manifolds by mathematicians such as Henri Poincaré, who introduced them in 1902, and later by John Munkres, who developed their theory. Manifolds are classified into several