The 1-skeleton of a G-manifold M is the set of points p ∈ M , where dimGp ≥ dimG − 1, and M is a GKM manifold if the dimension of this 1-skeleton is 2. M. Goresky, R. Kottwitz, and R. MacPherson show that for such a manifold this 1-skeleton has the structure of a “labeled” graph, ( , α), and that the equivariant cohomology ring ofM is isomorphic to the “cohomology ring” of this graph. Hence, if...

In this paper we will determine the multiple point manifolds of certain self-transverse immersions in Euclidean spaces. Following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold $V^5$ or a boundary. We will show there is an immersion of $S^7times P^2$ in $mathbb{R}^{1...

In this paper, we study deformations of coisotropic submanifolds in a symplectic manifold. First we derive the equation that governs C∞ deformations of coisotropic submanifolds and define the corresponding C∞-moduli space of coisotropic submanifolds modulo the Hamiltonian isotopies. This is a non-commutative and non-linear generalization of the well-known description of the local deformation sp...

Conventional discrete approximations of a manifold do not preserve its nontrivial topological features. In this article we describe an approximation scheme due to Sorkin which reproduces physically important aspects of manifold topology with striking delity. The approximating topological spaces in this scheme are partially ordered sets (posets). Now, in ordinary quantum physics on a manifold M ...

in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds r...

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.

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-...

Let Mm be an oriented manifold and let N a set consisting of closed manifolds the same odd dimension n. We consider topological space GN,M commutative diagrams. Each diagram consists few from that are mapped to M one point spaces pt each pair N. bordism group Ω⁎(GN,M)=⊕i=0∞Ωi(GN,M). introduce operations ⋆ [⋅,⋅] on Ω⁎(GN,M)⊗Q, make Ω⁎(GN,M)⊗Q into Z-graded (m−2n)-Poisson algebra. For N={S1} surf...

in this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper k-ideals. these definitions are thegeneralizations of the definitions of commutative, andimplicative hyper k-ideals, respectively, which have been definedin [12]. then we obtain some related results. in particular wedetermine the relationships between n-fold implicative hyperk-ideal and n-fold...

The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...