 See Atiyah–Segal completion theorem for more details.He defined new generalized homology and cohomology theories called bordism and cobordism, and pointed out that many of the deep results on cobordism of manifolds found by René Thom, C. T. C. Wall, and others could be naturally reinterpreted as statements about these cohomology theories.Some of these cohomology theories, in particular complex cobordism, turned out to be some of the most powerful cohomology theories known.