Differentiable Manifolds in Euclidean Space

Notes on Differentiable Manifolds

Double Point Manifolds of Immersions of Spheres in Euclidean Space

Anyone who has been intrigued by the relationship between homotopy theory and diierential topology will have been inspired by the work of Bill Browder. This note contains an example of the power of these interconnections. We prove that, in the metastable range, the double point manifold a self-transverse immersion S n # R n+k is either a boundary or bordant to the real projective space RP n?k. ...

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 ...

Note on the Embedding of Manifolds in Euclidean Space

M. Hirsch and independently H. Glover have shown that a closed ¿-connected smooth «-manifold M embeds in R2n~> if Mo immerses in A*""*-1, jè2k and 2/gra — 3. Here Mo denotes M minus the interior of a smooth disk. In this note we prove the converse and show also that the isotopy classes of embeddings of M in i?a"-»' are in one-one correspondence with the regular homotopy classes of immersions of...