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2013•Journal of Knot Theory and Its RamificationsRequires access

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

V. V. Sreedhar

Open publisher page 2 citations

Abstract

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 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 generalization of the Aharonov–Bohm effect in which charged particles moving through force-free regions are scattered by impenetrable, knotted solenoids.

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What this paper is about

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 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 generalization of the Aharonov–Bohm effect in which charged particles moving through force-free regions are scattered by impenetrable, knotted solenoids.

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Available abstract

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 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 generalization of the Aharonov–Bohm effect in which charged particles moving through force-free regions are scattered by impenetrable, knotted solenoids.

Key concepts: Knot complement, Knot (papermaking), Mathematics, Tricolorability, Quantum invariant, Knot invariant, Torus, Trefoil knot

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