Timeline for sphere bundles over spheres
Current License: CC BY-SA 3.0
4 events
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| Apr 14, 2014 at 18:45 | comment | added | Craig Westerland | More explicitly still: if $H$ is the tautological bundle over $S^2 = \mathbb{C} P^1$, then $H-1$ trivializes over $\infty$. Thus the $(p-1)$-fold external tensor power $(H-1)^{\otimes p-1}$ over $(S^2)^{\times p-1}$ descends to a virtual bundle over $(S^2)^{\wedge p-1} = S^{2p-2}$. Adding $n$ copies of the trivial bundle for large $n$ will eventually result in an actual vector bundle; the sphere bundle described above is the fibrewise 1-point compactification of this vector bundle. | |
| Apr 14, 2014 at 16:34 | comment | added | Craig Westerland | I should add: the fact that $\alpha$ is in the image of $J$ means that this fibration is in fact the fibrewise 1-point compactification of a vector bundle. | |
| Apr 14, 2014 at 16:28 | history | edited | Craig Westerland | CC BY-SA 3.0 |
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| Apr 14, 2014 at 16:10 | history | answered | Craig Westerland | CC BY-SA 3.0 |