Nontrivial tangent bundle that is diffeomorphic to the trivial bundle - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T03:08:04Z http://mathoverflow.net/feeds/question/58793 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/58793/nontrivial-tangent-bundle-that-is-diffeomorphic-to-the-trivial-bundle Nontrivial tangent bundle that is diffeomorphic to the trivial bundle Faisal 2011-03-17T23:25:39Z 2011-03-18T02:23:25Z <p>Is there an example of a smooth $n$-manifold $M$ whose tangent bundle is nontrivial as a bundle but is nonetheless (abstractly) diffeomorphic to the trivial bundle $M \times \mathbb{R}^n$?</p> <p>(This question was inspired by <a href="http://mathoverflow.net/questions/58685/trivial-fiber-bundle" rel="nofollow">http://mathoverflow.net/questions/58685/trivial-fiber-bundle</a>.)</p>