固定点集是■=1RP(2n)的对合

Involutions Fixing the Disjoint Union of Copies of Even Projective Space

<正> 本文给出:γ维流形上的对合,如果其不动点集F是有限个2n阶射影空间之并,那么若2n<r≠4n,则对合协边:若r=4n,则对合协边于(F×F,twist). 对实向量丛ξ~c→M(M~γ是流形),(N,ξ)∈N_m(BO)是由N→BO(·)→BO所确定,(RP(n),ξ)类中ξ经过N_n(BO)某Z:子空间的全部向量丛,(RP(n),ξ)+(RP(n),η)代表直和,由文献〔6〕知,如果λ→RP(n)为正规扭线丛,且n为偶数。

We show that any differentiable involution on a r-dimensional manifold(M,T) whose fixed point set F is a disjoint union of real projective spaces of constant dimension 2n,we have: if r=4n then (M,T)is bordant to (F×F, twist),if 2n〈r≠4n then (M,T) bounds.