不动点集为RP_1(2m)∪RP_2(2m)∪RP(1)的带有对合的光滑流形

Involutions Fixing the Disjoint Union of Projective Spaces RP_1(2m)∪RP_2(2m)∪RP(1)

设(Mr,T)是一个具有对合T的r(r>2m,m≠0)维光滑闭流形,它的不动点集为F。给出了F=RP1(2m)∪RP2(2m)∪RP(1)时对合的所有协边类,其中RP表示实射影空间。

Let （M^r,T） denote the smooth involution on the closed manifold M with fixed point set F. The bordism classes of the involutions with RP1（2m）∪RP2（2m）∪RP（1） are investigated. Here RP denotes the real projective space