Online Talk

The c_1-spherical bordism theory W was introduced in the work of E. Conner and P. Floyd on the torsion in the SU-bordism ring. It is the bordism theory of stably complex manifolds with the first Chern class induced from the sphere CP^1. This theory does not have a natural multiplication (since the Cartesian product of two c_1-spherical manifolds is not necessarily c_1-spherical), but it has a natural module structure over the SU-bordism. R. Stong defined an SU-bilinear multiplication on W via an SU-linear projection from the complex cobordism theory MU onto W, and used the resulting ring W to describe the torsion-free part of the SU-bordism ring. The Stong projection is one in the family of SU-linear projections MU -> W, each defining a complex orientation on W. Unlike W, the SU-bordism theory is not complex oriented.

In this talk, I will describe the algebra of SU-linear operations in complex cobordism, classify SU-linear projections and multiplications on W, the corresponding complex orientations and formal group laws on W, and prove the Landweber exactness of the W-theory.