I was reading recently about cobordism, and in specific about the Thom-Pontraygin theorem which states $\pi_{k}(S^n)$ is isomorphic to the cobordism classes of framed $n$-manifolds in $R^k$.
In relation to this, I also found mention of a group of framed bordism class, which I found to be denoted by $\Omega_i^{fr}$. However, I cannot seem to figure out what this means. I know a framing is some trivial bundle, but how big is the bundle (what dimension) if we talk about the framing of an $i$-manifold.
A definition of $\Omega_i^{fr}$ and an explanation of what it means would be much appreciated