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 2e-torsion lens space cannot be embedded in Euclidean space of dimension 4n-2α(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 2e-torsion lens spaces. Some of our best embeddings are within one dimension of being optimal.
Homology, Homotopy and Applications, Vol. 11 (2009), No. 2, pp.133-160.
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