Equivariant Embeddings in Euclidean Space

Embeddings of Surfaces in Euclidean Three-space

Embeddings and Immersions of Manifolds in Euclidean Space

The problem of computing the number of embeddings or immersions of a manifold in Euclidean space is treated from a different point of view than is usually taken. Also, a theorem dealing with the existence of an embedding of Mm in ä ¡s given. Introduction. This paper studies the existence and classification of differential immersions and embeddings of a differentiable manifold into Euclidean spa...

Tangent Bundle Embeddings of Manifolds in Euclidean Space

For a given n-dimensional manifold M we study the problem of finding the smallest integer N(M) such that M admits a smooth embedding in the Euclidean space R without intersecting tangent spaces. We use the Poincaré-Hopf index theorem to prove that N(S) = 4, and construct explicit examples to show that N(S) ≤ 3n + 3, where S denotes the n-sphere. Finally, for any closed manifold M, we show that ...

Equivariant Dierential Embeddings

Equivariant differential embeddings

Takens Dynamical Systems and Turbulence, Lecture Notes in Mathematics, edited by D. A. Rand and L. S. Young Springer-Verlag, New York, 1981 , Vol. 898, pp. 366–381 has shown that a dynamical system may be reconstructed from scalar data taken along some trajectory of the system. A reconstruction is considered successful if it produces a system diffeomorphic to the original. However, if the origi...