On embeddings in the sphere

Klein, John

doi:10.1090/S0002-9939-05-07823-8

On embeddings in the sphere
HTML articles powered by AMS MathViewer

by John R. Klein

Proc. Amer. Math. Soc. 133 (2005), 2783-2793

DOI: https://doi.org/10.1090/S0002-9939-05-07823-8

Published electronically: April 19, 2005

PDF | Request permission

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

William Browder, Embedding smooth manifolds, Proc. Internat. Congr. Math. (Moscow, 1966) Izdat. “Mir”, Moscow, 1968, pp. 712–719. MR 0238335
Francis X. Connolly and Bruce Williams, Embeddings up to homotopy type and geometric suspensions of manifolds, Quart. J. Math. Oxford Ser. (2) 29 (1978), no. 116, 385–401. MR 517733, DOI 10.1093/qmath/29.4.385
George Cooke, Embedding certain complexes up to homotopy type in euclidean space, Ann. of Math. (2) 90 (1969), 144–156. MR 242152, DOI 10.2307/1970685
George Cooke, Thickenings of CW complexes of the form $S^{m}\cup _{\alpha }e^{n}$, Trans. Amer. Math. Soc. 247 (1979), 177–210. MR 517691, DOI 10.1090/S0002-9947-1979-0517691-0
Octavian Cornea, New obstructions to the thickening of CW-complexes, Proc. Amer. Math. Soc. 132 (2004), no. 9, 2769–2781. MR 2054804, DOI 10.1090/S0002-9939-04-07345-9
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
Nathan Habegger, Embedding up to homotopy type—the first obstruction, Topology Appl. 17 (1984), no. 2, 131–143. MR 738942, DOI 10.1016/0166-8641(84)90037-3
Klein, J. R.: Moduli of suspension spectra. arXiv:math.AT/0210258, to appear in Trans. Amer. Math. Soc.
John R. Klein, Poincaré duality embeddings and fiberwise homotopy theory, Topology 38 (1999), no. 3, 597–620. MR 1670412, DOI 10.1016/S0040-9383(98)00034-2
Pascal Lambrechts, Don Stanley, and Lucile Vandembroucq, Embeddings up to homotopy of two-cones in Euclidean space, Trans. Amer. Math. Soc. 354 (2002), no. 10, 3973–4013. MR 1926862, DOI 10.1090/S0002-9947-02-03030-1
Mark Mahowald, The metastable homotopy of $S^{n}$, Memoirs of the American Mathematical Society, No. 72, American Mathematical Society, Providence, R.I., 1967. MR 0236923
Robert Rigdon, $p$-equivalences and embeddings of manifolds, J. London Math. Soc. (2) 2 (1975), no. 2, 233–244. MR 431211, DOI 10.1112/jlms/s2-11.2.233
C. T. C. Wall, Classification problems in differential topology. IV. Thickenings, Topology 5 (1966), 73–94. MR 192509, DOI 10.1016/0040-9383(66)90005-X
C. T. C. Wall, Surgery on compact manifolds, 2nd ed., Mathematical Surveys and Monographs, vol. 69, American Mathematical Society, Providence, RI, 1999. Edited and with a foreword by A. A. Ranicki. MR 1687388, DOI 10.1090/surv/069
Bruce Williams, Hopf invariants, localization and embeddings of Poincaré complexes, Pacific J. Math. 84 (1979), no. 1, 217–224. MR 559639