Edit: When I say cobordism, I mean oriented cobordism unless stated otherwise. Also note that I accidentally flip-flopped $\Omega^*$ and $\Omega_*$ — $\Omega^n$ should be cobordism classes of maps from manifolds of codimension $n$ to $X$, and $\Omega_n$ is cobordism classes of maps from manifolds of dimension $n$ to $X$.
Let’s say $M_1, M_2,$ and $X$ are differentiable manifolds. We have a map $f_1$, and a map $f_2$.
Let’s think of a movie: Continue reading Oriented Cobordism Cohomology