.2-torus Role With Cong Manifold Change With Side Sufficient Condition For Zero

In this paper we study under what condition a(Z₂)^k-vector bundle over a smooth closed manifold is equivariantly cobordant to zero.We use(φ,ηⁿ,M^m) to denote the action,the vector bundle and the manifold,respectively.Our 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 M^m＞2^k dim F;(3) each p-dimensional part F^p of the fixed point set possesses the linear independence property,then(φ,ηⁿ,M^m) is equivariantly cobordant to zero.Furthermore,we give an example to show that when dim M^m=2^k 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 iff the vector bundle is equivariantly cobordant to zero.