6533b857fe1ef96bd12b4edb
RESEARCH PRODUCT
KNOTS AND LINKS IN INTEGRABLE HAMILTONIAN SYSTEMS
J. Martínez AlfaroJ. CasasayasAna Nunessubject
Pure mathematicsAlgebra and Number TheoryIntegrable systemMathematical analysisMathematics::Algebraic TopologyMathematics::Geometric TopologyHamiltonian systemsymbols.namesakeMathematics::K-Theory and HomologySolid torussymbolsPeriodic orbitsHamiltonian (quantum mechanics)Mathematics::Symplectic GeometryMathematicsdescription
The main purpose of this paper is to prove that Bott integrable Hamiltonian flows and non-singular Morse-Smale flows are closely related. As a consequence, we obtain a classification of the knots and links formed by periodic orbits of Bott integrable Hamiltonians on the 3-sphere and on the solid torus. We also show that most of Fomenko's theory on the topology of the energy levels of Bott integrable Hamiltonians can be derived from Morgan's results on 3-manifolds that admit non-singular Morse-Smale flows.
year | journal | country | edition | language |
---|---|---|---|---|
1998-03-01 | Journal of Knot Theory and Its Ramifications |