不动点集为RP_1(2m)∪RP_2(2m)∪RP(2n+1)的对合

Involutions Fixing RP_1(2m)∪RP_2(2m)∪RP(2n+1)

设(Mr,T)是一个带有光滑对合T的r维光滑闭流形,考虑当对合的不动点集为F=RP1(2m)∪RP2(2m)∪RP(2n+1)(m≥1)时对合的协边分类.通过构造合适的对称多项式和计算示性数,证明了若r>2m+2n+2,则每个以F为不动点集的对合(Mr,T)协边.

Let（Mr,T） be a smooth closed manifold of dimension r with a smooth involution T,we investigate the bordism classes of the involutions with the fixed point set F=RP1（2m）∪RP2（2m）∪RP（2n＋1）（m≥1）.Constructing symmetric polynomial and computing characteristic number,we have proved that if r2m＋2n＋2,then every involution（Mr,T） fixing F bounds.