Timeline for Do covector fields correspond to homomorphisms of $ \mathscr C^\infty $-modules from the sheaf of vector fields to the sheaf of smooth functions?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14 at 0:03 | vote | accept | GeometriaDifferenziale | ||
| Jan 11 at 23:48 | comment | added | DamienC | Dimitri: you are right (and I'm totally wrong). Sheaves of sections are soft but not flabby. | |
| Jan 11 at 20:30 | answer | added | Dmitri Pavlov | timeline score: 2 | |
| Jan 11 at 20:10 | comment | added | Dmitri Pavlov | @DamienC: Flabby means the restriction morphism F(V)→F(U) is surjective for any inclusion of opens U⊂V. If F is the sheaf of sections of the trivial vector bundle, it is easy to construct examples where the restriction map is not surjective, e.g., the smooth section x↦1/x over (-∞,0)∪(0,∞) does not extend to the real line. | |
| Jan 11 at 17:23 | comment | added | DamienC | The "extension" you're looking for exists, because sheaves of sections of smooth vector bundles on smooth manifolds are flabby (they even are soft). Flabby means that the restriction morphisms are surjective. | |
| S Jan 11 at 15:38 | review | First questions | |||
| Jan 11 at 21:15 | |||||
| S Jan 11 at 15:38 | history | asked | GeometriaDifferenziale | CC BY-SA 4.0 |