Note on the embedding of manifolds in Euclidean space
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- by J. C. Becker and H. H. Glover PDF
- Proc. Amer. Math. Soc. 27 (1971), 405-410 Request permission
Abstract:
M. Hirsch and independently H. Glover have shown that a closed $k$-connected smooth $n$-manifold $M$ embeds in ${R^{2n - j}}$ if ${M_0}$ immerses in ${R^{2n - j - 1}},j \leqq 2k$ and $2j \leqq n - 3$. Here ${M_0}$ 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 ${R^{2n - j}}$ are in one-one correspondence with the regular homotopy classes of immersions of ${M_0}$ in ${R^{2n - j - 1}},j \leqq 2k - 1$ and $2j \leqq n - 4$.References
- P. E. Conner and E. E. Floyd, Fixed point free involutions and equivariant maps, Bull. Amer. Math. Soc. 66 (1960), 416–441. MR 163310, DOI 10.1090/S0002-9904-1960-10492-2 H. H. Glover, On embedding and immersing manifolds in euclidean space, Thesis, University of Michigan, Ann Arbor, Mich., 1967.
- André Haefliger, Plongements différentiables dans le domaine stable, Comment. Math. Helv. 37 (1962/63), 155–176 (French). MR 157391, DOI 10.1007/BF02566970
- André Haefliger and Morris W. Hirsch, Immersions in the stable range, Ann. of Math. (2) 75 (1962), 231–241. MR 143224, DOI 10.2307/1970171
- André Haefliger and Morris W. Hirsch, On the existence and classification of differentiable embeddings, Topology 2 (1963), 129–135. MR 149494, DOI 10.1016/0040-9383(63)90028-4
- Morris W. Hirsch, Embeddings and compressions of polyhedra and smooth manifolds, Topology 4 (1966), 361–369. MR 189051, DOI 10.1016/0040-9383(66)90034-6
- Ioan James and Emery Thomas, Note on the classification of cross-sections, Topology 4 (1966), 351–359. MR 212820, DOI 10.1016/0040-9383(66)90033-4
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 405-410
- MSC: Primary 57.20
- DOI: https://doi.org/10.1090/S0002-9939-1971-0268903-0
- MathSciNet review: 0268903