Stable extendibility and extendibility of vector bundles over lens spaces

A bstract . Firstly, we obtain conditions for stable extendibility and extendibility of complex vector bundles over the ð 2 n þ 1 Þ -dimensional standard lens space L n ð p Þ mod p , where p is a prime. Secondly, we prove that the complexification c ð t n ð p ÞÞ of the tangent bundle t n ð p Þ ð¼ t ð L n ð p ÞÞÞ of L n ð p Þ is extendible to L 2 n þ 1 ð p Þ if p is a prime, and is not stably extendible to L 2 n þ 2 ð p Þ if p is an odd prime and n b 2 p (cid:1) 2. Thirdly, we show, for some odd prime p and positive integers n and m with m > n , that t ð L n ð p ÞÞ is stably extendible to L m ð p Þ but is not extendible to L m ð p Þ .