Three-Manifolds
A three-manifold is a mathematical space that locally resembles three-dimensional Euclidean space. This means that around any point in a three-manifold, you can find a small neighborhood that looks like the familiar 3D space we experience in everyday life. Examples of three-manifolds include the surface of a sphere and a torus, which can be visualized as a doughnut shape.
Three-manifolds are studied in the field of topology, a branch of mathematics focused on the properties of space that are preserved under continuous transformations. They play a crucial role in various areas, including geometry, physics, and the study of knots. Understanding three-manifolds helps mathematicians explore complex structures and their relationships.