COMPLEX N-SPIN BORDISM OF SEMIFREE CIRCLE ACTIONS AND COMPLEX ELLIPTIC GENERA

We give a complete bordism analysis of rational bordism groups of semifree circle actions on complex N-Spin manifolds. Moreover, we introduce the notion of a complex N-Spin(c,t) manifold and give a characterization of cobordism groups of such manifolds which we use to compute the rational bordism groups of free circle actions of type t on complex N-Spin manifolds. Furthermore, we exploit this bordism analysis to furnish a mechanism with which we investigate a description, in terms of kernels of complex elliptic genera, of the ideal I*(N,t), generated by bordism classes of connected complex N-Spin manifolds admitting an effective circle action of type t, in the rational complex N-Spin cobordism ring Omega*(U,N) circle times Q.