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Simple physics ideas are used to derive an exact expression for a flat connection on the complement of a torus knot. The result is of some mathematical importance in the context of constructing representations of the knot group -- a topological invariant of the knot. It is also a step forward in the direction of obtaining a generalisation of the Aharonov-Bohm effect, in which charged particles moving through force-free regions are scattered by impenetrable, knotted solenoids.

AN EXACT EXPRESSION FOR A FLAT CONNECTION ON THE COMPLEMENT OF A TORUS KNOT