Geodesic
On the embedding dimension of 2-torsion lens spaces
Homology, homotopy, and applications, Tome 11 (2009) no. 2, pp. 133-160.

Voir la notice de l'article provenant de la source International Press of Boston

Using the ku- and BP-theoretic versions of Astey’s cobordism obstruction for the existence of smooth Euclidean embeddings of stably almost complex manifolds, we prove that, for $e$ greater than or equal to $α(n)$, the $(2n + 1)$-dimensional $2^e$-torsion lens space cannot be embedded in Euclidean space of dimension $4n − 2 α(n) + 1$. (Here $α(n)$ denotes the number of ones in the dyadic expansion of a positive integer $n$.) A slightly restricted version of this fact holds for $e α(n)$.We also give an inductive construction of Euclidean embeddings for $2^e$-torsion lens spaces. Some of our best embeddings are within one dimension of being optimal.
DOI : 10.4310/HHA.2009.v11.n2.a7
Classification : 19L41, 55S45, 57R40
Keywords: Euclidean embeddings of lens spaces, connective complex K-theory, Brown-Peterson theory, Euler class, modified Postnikov towers 
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Jesús González; Peter Landweber; Thomas Shimkus. On the embedding dimension of 2-torsion lens spaces. Homology, homotopy, and applications, Tome 11 (2009) no. 2, pp. 133-160. doi : 10.4310/HHA.2009.v11.n2.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n2.a7/

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