query: tangent bundle that isn't diffeomorphic to the Cartesian product
positive_passages.docid: 147547
positive_passages.text: Any example of manifold without global trivialization of tangent bundle
negative_passages.docid: 91322
negative_passages.text: A diffeomorphism whose tangent map preserves dot products is an isometry.
negative_passages.docid: 30597
negative_passages.text: Morphism that is not a mapping
negative_passages.docid: 153852
negative_passages.text: Example of modules that are projective but not free; torsion-free but not free
negative_passages.docid: 80418
negative_passages.text: The "Easiest" non-smoothable manifold
negative_passages.docid: 39487
negative_passages.text: Zariski Tangent Space and $k[\varepsilon]/\varepsilon^2$
negative_passages.docid: 156457
negative_passages.text: Show that $K[x,xy,xy^2,\dots]$ is not Noetherian
negative_passages.docid: 61373
negative_passages.text: A normal subgroup that is not a characteristic
negative_passages.docid: 129288
negative_passages.text: proof that topologist sine curve is not locally connected
negative_passages.docid: 67383
negative_passages.text: Prove that $G'$ is not planar.
negative_passages.docid: 92435
negative_passages.text: How to find two inequivalent ,but weakly equivalent bundles?
negative_passages.docid: 64084
negative_passages.text: Existence of a simple closed curve which is not null-homotopic
negative_passages.docid: 12772
negative_passages.text: A fiber bundle over Euclidean space is trivial.
negative_passages.docid: 80100
negative_passages.text: Boundary of product manifolds such as $S^2 \times \mathbb R$
negative_passages.docid: 2348
negative_passages.text: Show that the sphere, S, and $\mathbb{R}^2$ is not homeomorphic
negative_passages.docid: 136019
negative_passages.text: Vector bundle on a quadric $Q$
negative_passages.docid: 27757
negative_passages.text: $\mathbb{R}\to\mathbb{R}$ Diffeomorphism with special property