Topological Monodromy of an Integrable Heisenberg Spin Chain

Abstract

We investigate topological properties of a completely integrable system on S²×S²×S² which was recently shown to have a Lagrangian fiber diffeomorphic to RP³ 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.