七维透镜空间为不动点集的对合

The Involution Whose Fixed Point Set is 7-Lens Spaces

设 ( M7+ k,T)是光滑闭流形上的一个非平凡光滑对合 ,它的不动点集为 7维透镜空间 L3( p) .本文首先计算了 L 3( p)上任意向量丛的全 Stiefel-Whitney类 ,其次讨论了 ( M7+ k,T)的存在性 ,在存在的情形下 ,给出了带对合的流形 ( M7+ k,T) 协边类 .

Let (M 7+k ,T) be a smooth involution on a closed smooth manifold, whose fixed point set is L 3(p). In this paper, we calculate total Stiefel-Whitney classes of any vector bundle over the lens spaces L 3(p), study the existness of the involution (M 7+k ,T), and give their cobordism classes.