Quantum field theory whose amplitudes are determined by Topological propertyes and Knot invariants (often exclusively!)

E.g. knot invariant of the knots created space-time trajectories of particles/quasiparticles.

Kauffman invariant where $A$ is a phase

http://www.math.ru.nl/~mueger/TQFT/At.pdf

Many theories focus on 2+1 dimensions (2 space and 1 time)

Topological matter

Fractional quantum hall effect

Superconductor films

Superfluid films

Engineered super/spin-orbit systems. Majorana..