Timeline for Examples of the varying strengths of topological invariants
Current License: CC BY-SA 2.5
2 events
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| Jan 2, 2010 at 22:16 | comment | added | Jason DeVito - on hiatus | I just wanted to add that everything I wrote about $S^5$ bundles over $S^2$ applies equally well to $S^k$ bundles over $S^2$ for any $k\geq 3$, though for $k=4$ one must do a bit more work to make sure the ring structures on the two bundles agree. For $k=2$, the two total spaces are distinguished by their cohomology RING structure (but not groups). In fact, the unique nontrivial $S^2$ bundle over $S^2$ is diffeomorphic to $\mathbb{C}P^2$#$\overline{\mathbb{C}P^2}$, which Anton talks about below. | |
| Jan 2, 2010 at 18:49 | history | answered | Jason DeVito - on hiatus | CC BY-SA 2.5 |