Cobordism, Cohomology Theories and Formal Group Laws

We first explore the notion of G-manifold, cobordism and then discuss the generalized Pontrjagin-Thom Theorem. We then compute the cobordism rings Ω (...) using stable homotopy theory. Secondly, we investigate the relations between cohomology theories and formal group laws. This is the very beginning of the so called chromatic homotopy theory. For any complex oriented cohomology theories, we associate a formal group law. We show that the formal group law associated to complex cobordism is universal. Finally, for a suitable formal group law we give a way to realize it into a generalized homology theory.