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Results tagged with vector-bundles
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user 23571
A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.
5
votes
Do $\mathbb{HP}^2\#\overline{\mathbb{HP}^2}$ and $\mathbb{OP}^2\#\overline{\mathbb{OP}^2}$ a...
Another way of describing the content of the previous answers is as follows. Suppose one starts with one of the Hopf bundles $p:S^{2n-1}\to S^n$ for $n=2,4,8$ coming from $\mathbb C$, $\mathbb H$, or …
- 20k
13
votes
Accepted
How can I endow a "locally product" CW structure on a vector bundle over a CW complex?
The authors of this book are attempting to use CW structures to justify certain cohomology isomorphisms, but this seems to be the wrong approach since some of their claims about CW structures are just …
- 20k
6
votes
Accepted
Two set of axioms for Stiefel-Whitney classes
The naturality condition 1'' reduces the question of whether $v_1=w_1$ to the special case of the tautological bundles $\gamma_n$. In this case both $v_1$ and $w_1$ lie in $H^1(BO(n);{\mathbb Z}_2)$. …
- 20k
41
votes
Parallelizability of the Milnor's exotic spheres in dimension 7
Here's another way to answer the original question. There is a theorem of Bredon and Kosinski (Annals, 1966) which says that if a manifold $M^n$ is stably parallelizable, then either $M^n$ is parallel …
- 20k