Embedding punctured manifolds

Configuration Spaces on Punctured Manifolds

The object here is to study the following question in the homotopy theory of configuration spaces of a general manifold M : When is the fibration Fk+1(M) → Fr(M), r < k + 1, fiber homotopically trivial? The answer to this question for the special cases when M is a sphere or euclidean space is given in [4]. The key to the solution of the problem for compact manifolds M is the study of an associa...

Embedding arithmetic hyperbolic manifolds

We prove that any arithmetic hyperbolic n-manifold of simplest type can either be geodesically embedded into an arithmetic hyperbolic (n+ 1)-manifold or its universal mod 2 abelian cover can.

Embedding Multiple Manifolds

Many high dimensional data sets are characterized by a small number of degrees of freedom. Standard manifold-based dimensionality reduction techniques include the bias that all data lies on (or near) a single global manifold. Here we consider data sampled from multiple manifolds. We demonstrate a straightforward technique for multiple manifold embedding: the data is clustered, and each cluster ...

Isometric Embedding of Riemannian Manifolds

Embedding into Manifolds with Torsion

We introduce a class of special geometries associated to the choice of a differential graded algebra contained in Λ∗Rn. We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds that can be realized as submanifolds of a Riemannian manifold with special holonomy, to this more general context. In particular, we consider the case of hypersurfa...