Cartan equivalence

We solve the equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds via Cartan’s method of equivalence. The problem separates into two branches on total space, one of which ends up with the intransitive involutive structure equations. For the transitive case, we obtain an {e}-structure on both total and base spaces.

14p nutifooddau 21-01-2019 16 1   Download

This article is dedicated to solving the equivalence problem for a pair of third-order differential operators on the line under general fiber-preserving transformation using the Cartan method of equivalence. We will treat 2 versions of equivalence problems: First, the direct equivalence problem, and second, an equivalence problem to determine conditions on 2 differential operators such that there exists a fiber-preserving transformation mapping one to the other according to gauge equivalence.

10p tuongvidanh 06-01-2019 22 2   Download

We prove that a type II1 factor M can have at most one Cartan subalgebra A satisfying a combination of rigidity and compact approximation properties. We use this result to show that within the class HT of factors M having such Cartan subalgebras A ⊂ M , the Betti numbers of the standard equivalence relation associated with A ⊂ M ([G2]), are in fact isomorphism invariants for HT the factors M , βn (M ), n ≥ 0. The class HT is closed under amplifications HT HT and tensor products,

92p noel_noel 17-01-2013 37 7   Download