Topological Monodromy of an Integrable Heisenberg Spin Chain

Abstract

We investigate topological properties of a completely integrable system on $S^2\times S^2\times S^2$ which was recently shown to have a Lagrangian fiber diffeomorphic to $\mathbb{R}{P}^3$ not displaceable by a Hamiltonian isotopy [Oakley J., Ph.D. Thesis, University of Georgia, 2014]. This system can be viewed as integrating the determinant, or alternatively, as integrating a classical Heisenberg spin chain. We show that the system has non-trivial topological monodromy and relate this to the geometric interpretation of its integrals.

References in corpus (2)

• Rigid subsets of symplectic manifolds
• Toric degeneration and non-displaceable Lagrangian tori in $S^2\times S^2$