$SU$-linear operations in complex cobordism and $c_1$-spherical bordism theory

In the first part of the talk I will give a description of the set of $SU$-linear cohomological operations in complex cobordism and will show that they are generated by known geometrical operations $\partial_i$. Then I will talk about some properties of $c_1$-spherical bordism theory $W$, in particular, I will discuss $SU$-bilinear multiplications on $W$ and projections from complex cobordism onto $W$. At the end I will talk about complex orientations of $W$ and some particular results on the coefficients of the corresponding formal group laws.