Three-dimensional Topology

Three-dimensional topology is a branch of mathematics that studies the properties of three-dimensional spaces and shapes, focusing on their structure and how they can be transformed without tearing or gluing. It explores concepts like knots, surfaces, and how these objects can be manipulated. Think of it as understanding the different ways to connect and loop a piece of string in space, where the shape can twist and turn, but remains continuous. This field helps in various applications, from understanding the universe's shape to implications in physics and biology.