Embedding four manifolds in R7

On Embedding Circle-bundles in Four-manifolds

In this paper, we demonstrate an obstruction to finding certain splittings of four-manifolds along sufficiently twisted circle bundles over Riemann surfaces, arising from Seiberg-Witten theory. These obstructions are used to show a non-splitting result for algebraic surfaces of general type.

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...