Quantum topology is a branch of mathematics that combines concepts from quantum mechanics and topology. It studies the properties of spaces that remain unchanged under continuous transformations, while also incorporating the principles of quantum theory. This field explores how quantum states can be represented in topological spaces, leading to new insights in both mathematics and physics. Researchers in quantum topology often investigate knots and links, which are essential objects in topology. By applying quantum principles, they can analyze these structures in ways that classical topology cannot, revealing deeper connections between geometry, algebra, and quantum physics.