ИСТИНА

If we try to describe the structure of SU-bordisms of a point, intermediate groups W between SU-bordisms and complex bordisms naturally arise. In geometric terms W are groups of c1-spheric bordisms. Algebraically this groups are defined as the kernel of the cohomological operation in complex cobordism, but we can set the same groups as the image of some natural projections in unitary bordisms (idempotent cohomological operations). Using this projections one can define the multiplication on this groups (they are not subrings in the complex cobordism ring originally). In this case the forgetful homomorphism from SU-bordism to W becomes a ring homomorphism. I’m going to talk about such projections, the ring W, the connections between it and SU-bordism ring, and some further questions, such as, about interesting geometric representatives (with torus action, Calabi-Yau) of some important SU-bordism classes.