Abstract

In this paper we study the group J(L^k(n)) of stable fibre homotopy classes of vector bundles over the lens space, L^k(n) = S^2k+1 ∕ Z_n where Z_n is the cyclic group of order n. We establish the fundamental exact sequences and hence find the order of J(L^k(n)). We define a number N_k and prove that the inclusion-map i : L^k(n) → P_k(C) induces an isomorphism of J(P_k(C)) with the subgroup of J(L^k(n)) generated by the powers of the realification of the Hopf-bundle iff n is divisible by N_k. This provides the discrete approximation to the continuous case.

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