Non-immersion theorems for lens spaces. II

Abstract

for (zo, zu ..., zn) 6 S . The orbit space S2n+1/Zp is the lens space mod p and is written by L(p). It is a compact, connected, orientable C°°-manifold of dimension 2n + l and has the structure of a CJF-complex with one cell in each dimension 0, 1, ••-, 2n + l. Let LnQ(p) be the 2π,-skeleton of L (p). The purpose of this paper is to prove some results on the stable homotopy type of the stunted space L%(p)/L*g(p) (n>m) and on the non-immersibility of the lens space L\p) in the Euclidean space. After some preparations in §2, we determine the structure of the reduced Grothendieck ring K(L^(p)/LS(p)) of complex vector bundles in §3. Using the Adams operation we shall prove the following result in §4.