ИСТИНА

The c_1-spherical bordism theory W_* is an intermediate theory between complex and SU-bordisms and it plays an important role in calculations of the SU-bordism coefficient ring. There is no natural choice of multiplication on the theory W_* (since a direct product of two c_1-spherical manifolds doesn't have to be c_1-spherical). However, it turns out that the theory W_* is a direct summand in complex cobordism theory MU_*, and one can define a multiplication on W_* via projections. I will talk about SU-linear projections and multiplications on the theory W_*, as well as complex orientations of this theory, corresponding formal group laws and its Landweber exactness.