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,
Besana, A., Spera, M., On some symplectic aspects of knot framings, <<JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS>>, 2006; 15 (7): 883-912 [http://hdl.handle.net/10807/35977]
On some symplectic aspects of knot framings
Spera, Mauro
2006
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,I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.