Timeline for Open non-parallelizable 4-manifolds
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 16, 2016 at 22:50 | comment | added | Michael | Actually you just answered the second question, thank you. | |
| May 16, 2016 at 22:42 | vote | accept | Michael | ||
| May 16, 2016 at 22:39 | comment | added | Michael | Noted, I'll ask a separate question. | |
| May 16, 2016 at 22:39 | comment | added | Ryan Budney | To answer your 2nd question, perhaps the Wikipedia description of spin structures and characteristic classes would answer it? If your manifold is spin the tangent bundle trivializes over the 2-skeleton. It automatically trivializes over the 3-skeleton as $\pi_2 SO_4$ is trivial. Since its non-compact it admits a cell structure with no $4$-cells so you are done. | |
| May 16, 2016 at 22:39 | comment | added | Igor Belegradek | A classification of $SO(n)$ bundles with $n\le 4$ over a complex of dimension $\le 4$ is given by Dold-Whitney in maths.ed.ac.uk/~aar/papers/doldwhit.pdf, see Theorem 1. The classification is in terms of certain charactersitic classes which all vanish for open orientable spin manifolds. | |
| May 16, 2016 at 22:36 | comment | added | Ryan Budney | Generally it's considered bad form to change your question after it has been answered. It would be more appropriate to check Ruberman's answer as correct, and then post a follow-up (separate) question. | |
| May 16, 2016 at 22:17 | history | edited | Michael | CC BY-SA 3.0 |
added 116 characters in body
|
| May 16, 2016 at 21:58 | answer | added | Danny Ruberman | timeline score: 8 | |
| May 16, 2016 at 21:39 | history | edited | Michael | CC BY-SA 3.0 |
deleted 6 characters in body
|
| May 16, 2016 at 21:25 | history | asked | Michael | CC BY-SA 3.0 |