REIDEMEISTER TORSION OF PRODUCT MANIFOLDS AND QUANTUM ENTANGLEMENT OF PURE STATES WITH SCHMIDT RANK

Using symplectic chain complex, a formula for the Reidemeister torsion of product of oriented closed connected even dimensional manifolds is presented. In applications, the formula is applied to Riemann surfaces,Grassmannians, projective spaces and these results will be applied to manifolds of pure bipartite states with Schmidt ranks.