Oriented Cobordism Cohomology

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 $f_2$.

Screenshot from 2015-01-27 15:55:55

Let’s think of a movie: Continue reading Oriented Cobordism Cohomology