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On embeddings in the sphere
Author(s):
John
R.
Klein
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2783-2793.
MSC (2000):
Primary 55P25;
Secondary 57Q35
Posted:
April 19, 2005
MathSciNet review:
2146234
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Abstract:
We consider embeddings of a finite complex in a sphere. We give a homotopy-theoretic classification of such embeddings in a wide range.
References:
-
- [B]
- Browder, W.: Embedding smooth manifolds.
Proc. Internat. Congr. Math., (Moscow, 1966).
Izdat. ``Mir'', Moscow 712-719 (1968) MR 0238335 (38:6611) - [C-W]
- Connolly, F. X., Williams, B.: Embeddings up to homotopy type and geometric suspensions of manifolds.
Quart. J. Math. Oxford 29, 385-401 (1978) MR 0517733 (83a:57022) - [Co1]
- Cooke, G.: Embedding certain complexes up to homotopy type in euclidean space.
Ann. of Math. 90, 144-156 (1969) MR 0242152 (39:3486) - [Co2]
- Cooke, G.: Thickenings of CW complexes of the form
 .
Trans. Amer. Math. Soc. 247, 177-210 (1979) MR 0517691 (81c:55016) - [Cor]
- Cornea, O.: New obstructions to the thickening of CW complexes.
Proc. Amer. Math. Soc. 132, 2769-2781 (2004) MR 2054804 - [H-H]
- Haefliger, A., Hirsch, M. W.: On the existence and classification of differentiable embeddings.
Topology 2, 129-135 (1963) MR 0149494 (26:6981) - [Ha]
- Habegger, N.: Embedding up to homotopy type--the first obstruction.
Topology Appl. 17, 131-143 (1984) MR 0738942 (85e:57022) - [Kl1]
- Klein, J. R.: Moduli of suspension spectra.
arXiv:math.AT/0210258,
to appear in Trans. Amer. Math. Soc. - [Kl2]
- Klein, J. R.: Poincaré embeddings and fiberwise homotopy theory.
Topology 38, 597-620 (1999) MR 1670412 (2000b:57037) - [L-S-V]
- Lambrechts, P., Stanley, D., Vandembroucq, L.: Embeddings up to homotopy of two-cones in Euclidean space.
Trans. Amer. Math. Soc. 354, 3973-4013 (2002) MR 1926862 (2003h:55012) - [Ma]
- Mahowald, M.: The metastable homotopy of
 .
(Memoirs of the Amer. Math. Soc., Vol. 27).
Amer. Math. Soc. 1967 MR 0236923 (38:5216) - [Ri]
- Rigdon, R.:
 -equivalences and embeddings of manifolds.
J. London Math. Soc. 2 (1975) MR 0431211 (55:4213) - [St]
- Stallings, J. R.: Embedding homotopy types into manifolds.
1965 unpublished paper (see http://math.berkeley.edu/ stall for a TeXed version) - [Wa1]
- Wall, C. T. C.: Classification problems in differential topology--IV. Thickenings.
Topology 5, 73-94 (1966) MR 0192509 (33:734) - [Wa2]
- Wall, C. T. C.: Surgery on Compact Manifolds.
(Mathematical Surveys and Monographs, Vol. 69).
Amer. Math. Soc. 1999 MR 1687388 (2000a:57089) - [Wi]
- Williams, B.: Hopf invariants, localizations, and embeddings of Poincaré complexes.
Pacific J. Math. 84, 217-224 (1979) MR 0559639 (81e:57023)
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Additional Information:
John
R.
Klein
Affiliation:
Department of Mathematics, Wayne State University, Detroit, Michigan 48202
Email:
klein@math.wayne.edu
DOI:
10.1090/S0002-9939-05-07823-8
PII:
S 0002-9939(05)07823-8
Received by editor(s):
October 29, 2003
Received by editor(s) in revised form:
May 1, 2004
Posted:
April 19, 2005
Additional Notes:
The author was partially supported by NSF Grant DMS-0201695
Communicated by:
Paul Goerss
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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