Timeline for Riemannian version of topological $K$-theory
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Aug 17, 2020 at 21:32 | comment | added | Qiaochu Yuan | Said another way, the space of Riemannian metrics on a given vector bundle is convex, hence contractible. So the natural forgetful map from Riemannian vector bundles to vector bundles has contractible fibers. | |
| Aug 17, 2020 at 20:19 | comment | added | mme | Two Riemannian vector bundles are (1)-equivalent iff they are isomorphic as vector bundles, so you can get nothing new from this. One way of thinking of this is the fact that a Riemannian vector bundle is classified by a map to $BO(n)$, while a vector bundle is classified by a map to $BGL(n)$. Because the inclusion $O(n) \to GL(n)$ is a homotopy equivalence the induced map on classifying spaces is too. | |
| Aug 17, 2020 at 18:11 | history | asked | Ali Taghavi | CC BY-SA 4.0 |