A homology «-manifold is a space which has the same local homology at each point as Euclidean n-space. The principal result of this paper is the characterization of triangulable homology manifolds by a global property: The rc-circuit X is a homology manifold if and only if the diagonal cycle A in X x X is Poincare dual to a cocycle with support A (Theorem 1). If X is a smooth manifold, this coc...

Let 2 be a manifold and X, Yr , Ya equidimensional submanifolds, all intersecting at 0 E X. Y, and Yz are said to be contact eqil&.~lent (r&A respect to X) at 0 if there exists a germ of diffeomorphism f: (2, 0) + (Z, 0) mapping X into X and Yr into Yz . The notion of contact equivalence is due to John Mather and plays an important role in his theory of singularities of differentiable mappings....

The formality theorem for Hochschild chains of the algebra of functions on a smooth manifold gives us a version of the trace density map from the zeroth Hochschild homology of a deformation quantization algebra to the zeroth Poisson homology. We propose a version of the algebraic index theorem for a Poisson manifold which is based on this trace density map. 1991 MSC: 19K56, 16E40.

A theory of tubular neighborhoods for strata in manifold stratified spaces is developed. In these topologically stratified spaces, manifold stratified approximate fibrations and teardrops play the role that fibre bundles and mapping cylinders play in smoothly stratified spaces. Applications include a multiparameter isotopy extension theorem, neighborhood germ classification and a topological ve...

Mean curvature flow evolves isometrically immersed base Riemannian manifolds M in the direction of their mean curvature in an ambient manifold M̄ . We consider the classical solutions to the mean curvature flow. If the base manifold M is compact, the short time existence and uniqueness of the mean curvature flow are well-known. For complete noncompact isometrically immersed hypersurfaces M (unif...

In this paper,we deeply research Lagrange interpolation of n-variables and give an application of Cayley-Bacharach theorem for it. We pose the concept of sufficient intersection about s(1 ≤ s ≤ n) algebraic hypersurfaces in n-dimensional complex Euclidean space and discuss the Lagrange interpolation along the algebraic manifold of sufficient intersection. By means of some theorems ( such as Bez...

We use convex decomposition theory to (1) reprove the existence of a universally tight contact structure on every irreducible 3-manifold with nonempty boundary, and (2) prove that every toroidal 3-manifold carries infinitely many nonisotopic, nonisomorphic tight contact structures. It has been known for some time that there are deep connections between the theory of taut foliations and tight co...