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The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
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What does Robert Stong mean when he says $H^*(MO(k))$ is a free Steenrod algebra in dimensio...
First, let's clarify what the statement means:
The Steenrod algebra is a graded algebra, and $H^*(X)$ for any spectrum $X$ is a graded module over it. This means that the action $\mathcal{A}_2\otimes …