Timeline for Examples of non-diffeomorphic smooth manifolds with diffeomorphic tangent bundle
Current License: CC BY-SA 2.5
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| Jul 13, 2010 at 18:32 | history | edited | Igor Belegradek | CC BY-SA 2.5 |
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| Jul 13, 2010 at 18:30 | comment | added | Igor Belegradek | @Tom, I think example 4 works even when the tangent bundle to $M$ is not stably trivial. The conclusion will be that there are infinitely many manifolds $M_i$ in the simple homotopy type of $M$ that all $M_i$'s have diffeomorphic tangent bundles. I am not sure how to get them diffeomorphic to $TM$ though (in fact, this may be a hasty claim in my original answer , so I will edit it accordingly). Also in example 2 most bundles are nontrivial I think (as spheres are only parallelizable in dimensions 1, 3, 7). | |
| Jul 13, 2010 at 17:16 | comment | added | Tom Church | These examples are great! Do you know any examples of non-homeomorphic closed manifolds whose tangent bundles are nontrivial and diffeomorphic? | |
| Jul 13, 2010 at 15:30 | vote | accept | user47274 | ||
| Jul 13, 2010 at 15:23 | history | answered | Igor Belegradek | CC BY-SA 2.5 |