Quantum topology

Quantum topology is a branch of mathematics that connects quantum mechanics with low-dimensional topology.

Dirac notation provides a viewpoint of quantum mechanics which becomes amplified into a framework that can embrace the amplitudes associated with topological spaces and the related embedding of one space within another such as knots and links in three-dimensional space. This bra–ket notation of kets and bras can be generalised, becoming maps of vector spaces associated with topological spaces that allow tensor products.^[1]

Topological entanglement involving linking and braiding can be intuitively related to quantum entanglement.^[1]

See also

• Topological quantum field theory
• Reshetikhin–Turaev invariant