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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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Continuous self-maps of the plane are semiconjugate or conjugate?

Let $f : X → X$ and $g : Y → Y$ be continuous functions. We say that $f$ and $g$ are topologically conjugate if there exists a homeomorphism $α : X → Y$ such that $$f∘α=α∘g$$. A related idea is the n …