Nonimmersion of lens spaces with 2-torsion

Abstract

From a study of the equivariant unitary K-theory of the Stiefel manifold V k + 1 , 2 ( C ) {V_{k + 1,2}}({\mathbf {C}}) , it is shown that the lens space L k ( n ) {L^k}(n) , with n a multiple of 2 2 k − 1 − α ( k − 1 ) {2^{2k - 1 - \alpha (k - 1)}} , does not immerse in Euclidean space of dimension 4 k − 2 α ( k ) − 2 4k - 2\alpha (k) - 2 .