The present article delves into some symplectic features arising in basic knot theory. An interpretation of the writhing number of a knot (with reference to a plane projection thereof) is provided in terms of a phase function analogous to those encountered in geometric optics, its variation upon switching a crossing being akin to the passage through a caustic, yielding a knot theoretical analogue of Maslov's theory. A novel derivation of the Feynman-Onsager relation is provided. A geometrical setting for the ground state wave functions appearing in the theory of the Fractional Quantum Hall effect is provided,
On some symplectic aspects of knot framings
SPERA, Mauro
2006-01-01
Abstract
The present article delves into some symplectic features arising in basic knot theory. An interpretation of the writhing number of a knot (with reference to a plane projection thereof) is provided in terms of a phase function analogous to those encountered in geometric optics, its variation upon switching a crossing being akin to the passage through a caustic, yielding a knot theoretical analogue of Maslov's theory. A novel derivation of the Feynman-Onsager relation is provided. A geometrical setting for the ground state wave functions appearing in the theory of the Fractional Quantum Hall effect is provided,
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