Number of fixed points for unitary T^n-1-manifold

Let M be a 2n-dimensional closed unitary manifold with a T^n-1- action with only isolated fixed points. In this paper, we first prove that the equivariant cobordism class of a unitary T^n-1-manifold M is just determined by the equivariant Chern numbers C^Tn-1/ω[M], where ω=(i1,i2,…,i6)are the multi-indexes for all i1,i2,…,i6∈N. Then we show that if M does not bound equivariantly, then the number of fixed points is greater than or equal to [n/6]+ 1, where [n/6] denotes the minimum integer no less than n/6.