酉S^(1)流形的Todd亏格与A_(k)亏格

Todd Genus and A_(k)-Genus of Unitary S^(1)-Manifolds

假设M是紧连通的2n维酉流形,M上存在非平凡的保复结构的圆周群作用.如果M的第一陈类等于k_(0)x,其中x为某二维整系数上同调类,|k_(0)|≥n+2,且M的一维整系数上同调群为零,证明了M的Todd亏格和A_(k)亏格为零,k≥2.

Assume that M is a compact connected unitary 2 n-dimensional manifold and admits a nontrivial circle action preserving the given complex structure.If the first Chern class of M equals to k_(0)x for a certain 2^(nd)integral cohomology class x with|k_(0)|≥n+2,and its first integral cohomology group is zero,this short paper shows that the Todd genus and A_(k)-genus of M vanish,k≥2.