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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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Minimal radius of a ball admitting a trivialization of a vector bundle

Let $X$ be a compact Hausdorff space and $p : V \to X$ a complex vector bundle of rank $n$. For $r > 0$ let $B(r,x)$ denote the open ball of radius $r$ around $x$. Does there exist an $r$ such that, f …
Francine Laporte's user avatar