闭流形上向量丛的（Z2）k群作用

（Z2）k-vector Bundle over a Smooth Closed Manifold

给出了光滑范畴下带有（Z2）k群作用的闭流形上向量丛等变配边于零的一个充分条件：闭流形的维数大于2k倍不动点集的维数；不动点集的Stiefel—Whitney类为零；不动点集的分支满足线性独立条件．同时在闭流形的维数等于2k倍不动点集的维数的情况下，如果再进一步加强条件为向量丛配边为零，则向量丛等变配边于零．

A sufficient condition, under which a （Zz）k-vector bundle over a smooth closed manifold is equivariantly cobordant to zero, is obtained. （Ф,ηn,Mm） denotes the action, the vector bundle and the manifold, respectively. The main result is stated as follows： if （1） all Stiefel-Whitney classes of the tangent bundle to each connected component of the fixed point set F vanish in positive dimension; （2） dim Mm〉2kdim F; （3） each p-dimensional part Fp of the fixed point set possesses the linear independence property, then （Ф,ηn,Mm）is equivariantly cobordant to zero. Furthermore, an example is given to show that when dim Mn= 2k dim F and other two conditions are still satisfied, the vector bundle still may be not equivariantly cobordant to zero. In this case the vector bundle is cobordant to zero if and only if the vector bundle is equivariantly cobordant to zero.