commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

We discuss the dynamics of a particular two-dimensional (2D) physical system in the four dimensional (4D) (non-)commutative phase space by exploiting the consistent Hamiltonian and Lagrangian formalisms based on the symplectic structures defined on the 4D (non-)commutative cotangent manifold. The noncommutativity exists in the coordinates or the momentum planes embedded in the 4D cotangent mani...

The present paper is a continuation of [Oh2] and [GL] devoted to the study of finite type invariants of integral homology 3-spheres. We introduce the notion of manifold weight systems, and show that type m invariants of integral homology 3-spheres are determined (modulo invariants of type m − 1) by their associated manifold weight systems. In particular we deduce a vanishing theorem for finite ...

Given a circle-valued Morse function of a closed oriented manifold, we prove that Reidemeister torsion over a non-commutative formal Laurent polynomial ring equals the product of a certain non-commutative Lefschetz-type zeta function and the algebraic torsion of the Novikov complex over the ring. This paper gives a non-commutative generalization of the result of Hutchings-Lee on the abelian set...

In this paper we provide a non-commutative version of the fundamental class [dM ] = [(L 2(M,Λ∗(T ∗M)), d+ d∗, ε)] of a smooth closed Riemannian manifold M . The formulation involves elements of A. Connes’ non-commutative geometry, G. Kasparov’s KK-theory and the standard theory of von Neumann algebras. Using axioms based on [C1], it is proved we can recover the ordinary differential geometry of...

In this paper we provide a non-commutative version of the fundamental class [dM ] = [(L 2(M,Λ∗(T ∗M)), d+ d∗, ε)] of a smooth closed Riemannian manifold M . The formulation involves elements of A. Connes’ non-commutative geometry, G. Kasparov’s KK-theory and the standard theory of von Neumann algebras. Using axioms based on [C1], it is proved we can recover the ordinary differential geometry of...

Quantization, at least in some formulations, involves replacing some algebra of observables by a (more non-commutative) deformed algebra. In view of the fundamental role played by K-theory in non-commutative geometry and topology, it is of interest to ask to what extent K-theory remains “rigid” under this process. We show that some positive results can be obtained using ideas of Gabber, Gillet-...

We show an analogous result of the famous Tits alternative for a group G of birational automorphisms of a projective hyperkäher manifold: Either G contains a non-commutative free group or G is an almost abelian group of finite rank. As an application, we show that the automorphism groups of the so-called singular K3 surfaces contain non-commutative free groups.

We establish the equality between the restriction of the Adler-ManinWodzicki residue or non-commutative residue to pseudodifferential operators of order n on an n-dimensional compact manifold M, with the trace which J. Dixmier constructed on the Macaev ideal. We then use the latter trace to recover the Yang Mills interaction in the context of non-commutative differential geometry.