On some symplectic aspects of knot framings

Mauro Spera, Alberto Besana

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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,
Original languageEnglish
Pages (from-to)883-912
Number of pages30
JournalJournal of Knot Theory and its Ramifications
Volume15
Publication statusPublished - 2006

Keywords

  • Framing of knots, symplectic geometry, Chern-Simons action

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