An example on embedding up to homotopy type
Author:
Elmer Rees
Journal:
Proc. Amer. Math. Soc. 26 (1970), 217-218
MSC:
Primary 55.70
DOI:
https://doi.org/10.1090/S0002-9939-1970-0263080-3
MathSciNet review:
0263080
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Abstract | References | Similar Articles | Additional Information
Abstract: A finite complex $K$ is constructed with the following property. $K \vee {S^r}$ embeds in ${R^n}$ up to homotopy type but $K$ does not.
- J. F. Adams, Vector fields on spheres, Ann. of Math. (2) 75 (1962), 603–632. MR 139178, DOI https://doi.org/10.2307/1970213
- George Cooke, Embedding certain complexes up to homotopy type in euclidean space, Ann. of Math. (2) 90 (1969), 144–156. MR 242152, DOI https://doi.org/10.2307/1970685
- I. M. James and J. H. C. Whitehead, The homotopy theory of sphere bundles over spheres. I, Proc. London Math. Soc. (3) 4 (1954), 196–218. MR 61838, DOI https://doi.org/10.1112/plms/s3-4.1.196 S. P. Novikov, The topology summer institute (Seattle, Wash., 1963), Uspehi Mat. Nauk 20 (1965), no. 1 (121), 147-169 = Russian Math. Surveys 20 (1965), no. 1, 145-167.
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Additional Information
Keywords:
Embedding up to homotopy type,
complex Stiefel manifolds
Article copyright:
© Copyright 1970
American Mathematical Society