On the classification of $(n-k+1)$-connected embeddings of $n$-manifolds into $(n+k)$-manifolds in the metastable range
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- by Rong Liu PDF
- Trans. Amer. Math. Soc. 347 (1995), 4245-4258 Request permission
Abstract:
For an $(n - k + 1)$-connected map $f$ from a connected smooth $n$-manifold $M$ to a connected smooth $(n + k)$-manifold $V$, where $M$ is closed, we work out the isotopy group ${[M \subset V]_f}$ in the metastable range $n \leqslant 2k - 4$. To prove our results, we develop the Hurewicz-type theorems which provide us with the efficient methods of computing the homology groups with local coefficients from the homotopy groups.References
- Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
- Jean-Pierre Dax, Étude homotopique des espaces de plongements, Ann. Sci. École Norm. Sup. (4) 5 (1972), 303–377 (French). MR 321110, DOI 10.24033/asens.1230
- Nathan Habegger, Obstructions to embedding disks. II. A proof of a conjecture of Hudson, Topology Appl. 17 (1984), no. 2, 123–130. MR 738941, DOI 10.1016/0166-8641(84)90036-1
- 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
- André Haefliger, Plongements différentiables de variétés dans variétés, Comment. Math. Helv. 36 (1961), 47–82 (French). MR 145538, DOI 10.1007/BF02566892
- André Haefliger, Plongements différentiables dans le domaine stable, Comment. Math. Helv. 37 (1962/63), 155–176 (French). MR 157391, DOI 10.1007/BF02566970 —, Plongements de variétés dans le domaine stable, Seminaire Bourbaki, 150, no. 245 (1962/63).
- 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
- Allen Hatcher and Frank Quinn, Bordism invariants of intersections of submanifolds, Trans. Amer. Math. Soc. 200 (1974), 327–344. MR 353322, DOI 10.1090/S0002-9947-1974-0353322-6
- J. F. P. Hudson, Piecewise linear embeddings, Ann. of Math. (2) 85 (1967), 1–31. MR 215308, DOI 10.2307/1970522
- Lawrence L. Larmore, Isotopy groups, Trans. Amer. Math. Soc. 239 (1978), 67–97. MR 487040, DOI 10.1090/S0002-9947-1978-0487040-4 Liu Rong, On the classification of embeddings of $n$-manifolds into $2n$-manifolds in the same regular homotopy class (to appear). H. A. Salomonsen, On the existence and classification of differential embeddings in the metastable range, Aarhus mimeographed notes, 1973.
- Robert M. Switzer, Algebraic topology—homotopy and homology, Die Grundlehren der mathematischen Wissenschaften, Band 212, Springer-Verlag, New York-Heidelberg, 1975. MR 0385836, DOI 10.1007/978-3-642-61923-6
- 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
- George W. Whitehead, Homotopy theory, Massachusetts Institute of Technology, Mathematics Department, Cambridge, Mass., 1953. Compiled by Robert J. Aumann. MR 0091469
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 4245-4258
- MSC: Primary 57N35; Secondary 55Q05
- DOI: https://doi.org/10.1090/S0002-9947-1995-1290732-0
- MathSciNet review: 1290732