All Questions
7 questions
8
votes
2
answers
578
views
Maximal trivialising subspace for a vector bundle
Let $X$ be a locally compact Hausdorff space. Given a vector bundle $p: E\to X$, a subspace $Y$ of $X$ is called trivialising (for this bundle), if after restricting this bundle to $Y$, it is a ...
- 403
7
votes
1
answer
557
views
Continuous maps $f:S^n \to \mathbb{C}P^m$ with $f(x)\perp f(-x) $
Question 1: What is a complete classification of all positive integers $m,n$ with the following property:
There is a continuous map $f:S^n \to \mathbb{C}P^m$ such that $f$ maps antipodal ...
- 356
7
votes
0
answers
119
views
The automorphism group of the fibered cylinder
My collegue (Oleg Gutik) is interested in finding a proper reference to a description of the group $G$ of homeomorphisms $h:\mathbb T\times\mathbb R\to\mathbb T\times\mathbb R$ of the cylinder that ...
- 41.8k
4
votes
3
answers
767
views
A natural embedding of the total space of tautological bundle over $G(2,n)$ in $G(2,n+1)$
I learned from the following post that the total space of the tautological line bundle over $\mathbb{R}P^{n}$ is diffeomorphic to $\mathbb{R}P^{n+1}\setminus \{pt\}$.(There is a natural embedding$([x]...
- 356
2
votes
1
answer
179
views
Factorization systems for vector bundles
Are there any well-known factorization systems for the category of vector bundles defined over topological spaces?
- 615
1
vote
1
answer
143
views
Gluing locally defined continous functions over complex domain
This is a cross-post to the question I asked at MSE over almost a month ago.
Suppose $n, l, m \in \mathbb N$ and $n \ge l > m$. Let $T: \mathbb C \to \mathcal M(n \times l; \mathbb C)$ be ...
- 195
1
vote
0
answers
111
views
Unique Hausdorff topology on trivial vector bundle?
Question: Is there a Hausdorff topology other than the product topology on $X\times \mathbb{C}^n$, that turns $(X\times \mathbb{C}^n, \mathrm{pr}_1)$ into a vector bundle, where $\mathrm{pr_1}$ ...
- 11