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Eric Canton's user avatar
Eric Canton's user avatar
Eric Canton
  • Member for 11 years, 3 months
  • Last seen more than 1 year ago
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Why C*-algebras is not as popular as other areas of pure mathematics?
In addition to the already mentioned schools, the University of Nebraska has at least 3 professors working in $C^*$-algebras, including a new hire: Chris Schaffhauser, who did a postdoc at Waterloo. UNL also has an active group of graduate students who hold learning seminars.
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A characterization of round sphere
I missed that. I'll leave my comment for other uncareful readers.
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A characterization of round sphere
Isn't this property you assume also true for $k$-planes (edit: meaning affine-linear subspaces) embedded in $\mathbb{R}^{k+1}$?
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Local isometry implies covering map: nonempty boundary case
Or, less complicated: take $f: M \to N$ to be the cylinder $M = [0, 1/2] \times \mathbb{S}^1$ including into $N = [0, 1] \times \mathbb{S}^1$.
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Local isometry implies covering map: nonempty boundary case
@EduardoLonga: could one not use the same idea for a riemannian manifold with two isomorphic boundary components, gluing just one? More specifically, I'm thinking of a cylinder $[0, 1] \times \mathbb{S}^1$, and gluing two of these: one along $\{0\} \times \mathbb{S}^1$ and the other along $\{1\} \times \mathbb{S}^1$.
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Integral of matrix determinant with respect to Lebesgue measure
Could you possibly remind us what $\|\cdot\|_F$ is?
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Can we recover all $k$-minors of a square matrix from some of them?
Why do you need the non-degeneracy condition? Aren't you assuming $A$ is invertible?
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Flat algebra over polynomial ring
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Are torsion-free rank 1 modules over integral schemes line bundles?
Any coherent sheaf of ideals on an integral scheme is rank one and torsion free.
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Locus of trivialization of an extension of a vector bundle
It seems strange that $j_*\mathcal{E}$ would be a coherent $\mathcal{O}_X$-module. Of course, this is quasi-coherent, but $j$ is not proper (unless $X \setminus U$ is empty...) so coherent sheaves on $U$ don't go to coherent sheaves on $X$. Do you mean there is some vector bundle $\mathcal{E}'$ on $X$ that restricts to $\mathcal{E}$ on $U$? (e.g. as in Hartshorne Ex. II.5.15?)