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Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].

3 votes

Lie Semigroups?

Much of the literature on the representation theory of the group $GL_n$ is really about the representation theory of the monoid $M_n$. (One might argue that it's really about the representation theory …
Allen Knutson's user avatar
20 votes

Unifying Geometry for Characteristic Classes

I would compare at least 2 & 3, if not 4, using maps into classifying spaces. For a space $X$ homotopic to a finite CW-complex (at least), the pullback map $Map(X,Gr_n(\mathbb C^\infty)) \to \{$isomo …
Allen Knutson's user avatar