不动点集为有限个奇数维复射影空间并的对合

Involutions of the Disjoint Union of Fixed Point Set with Odd-Dimensional Complex Projective Spaces

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有限个奇数维复射影空间的并,即F=∪i=1t∪j=1miCPj(ni())(ni为奇数)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,on the basis of which we investigated the bordism classes of the involutions of a disjoint union of fixed point set with odd-dimensional complex projective spaces,i.e.,F = ∪i=1t∪j=1miCPj（ni（））（niis odd）.Constructing symmetric polynomial and computing characteristic number,we proved every involution（Mr,T）of fixed Fbounds.