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Results tagged with dg.differential-geometry
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user 83633
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
3
votes
Accepted
$E \times_H \mathbb{R}^n$ is isomorphic to the total space of the tautological bundle $\gamm...
Write an element of $GL(n+k,\mathbb R)$ as $\begin{pmatrix}C & D\\ E& F\end{pmatrix}$, then the principal $H$-bundle sends this element to $\rm{Im}\begin{pmatrix}C \\ E\end{pmatrix}$ in the Grassmanni …
- 666
14
votes
Accepted
embedding of quaternionic projective spaces
I. M. James, Lectures on algebraic and differential topology, pp. 134–174, Lecture Notes in Math., Vol. 279, Springer, Berlin, 1972,
Theorems 1.2 and 1.3 show that $$N=13.$$
- 666
0
votes
Tameness in $\mathbb{R}^{n^2}$ of the subset consisting of matrices of positive determinant
This applies to the earlier version of the question:
It is an open subset since the determinant function is continuous, and open subsets are locally path-connected.
- 666
0
votes
Tameness in $\mathbb{R}^{n^2}$ of the subset consisting of matrices of positive determinant
One way is to reduce first to $x,y$ with $n$ distinct complex eigenvalues. Then the $n$ eigenvalues and eigenspaces of x are close to those of y. Now connect all those with paths (just make sure not t …
- 666