ИСТИНА

I will talk about the theory of c1-spherical bordisms W - an intermediate theory between complex and special unitary bordisms, which is an important tool to describe the ring of coefficients of the latter one. On the one hand, this theory is a direct summand in complex bordism and does not have one natural multiplication, but admits a whole family of multiplications. Some of them are defined using projections from complex bordisms onto the direct summand W. On the other hand, using projections one can define a complex orientation on W, in contrast to the theory of SU-bordisms. In my talk I will discuss in more detail multiplications, projections and complex orientations on W, as well as the corresponding formal group laws.