New posts in vector-bundles

When is the pushforward / direct image of a reflexive sheaf locally free?

algebraic-geometry commutative-algebra sheaf-theory vector-bundles

Are vector bundles on $\mathbb{P}_{\mathbb{C}}^n$ of any rank completely classified? (main interest $n=3$)

reference-request algebraic-geometry complex-geometry vector-bundles

Projection of fiber bundle is a submersion

geometry differential-geometry riemannian-geometry vector-bundles fiber-bundles

Is a space with no nontrival vector bundles contractible?

algebraic-topology vector-bundles

Rank $n$ vector bundle with $n$ pointwise linearly independent sections is trivial

vector-bundles

Is there a fibre bundle with fibre homeomorphic to $\mathbb R^k$ which cannot be given the structure of a vector bundle?

geometry differential-geometry vector-bundles fiber-bundles

Pull-back of sections of vector bundles

algebraic-geometry vector-bundles

Understanding the canonical line bundle $H$, and the fact that $(H \otimes H)\oplus 1 \simeq H \oplus H$

vector-bundles

Explicit formula for the curvaure of a connection

differential-geometry vector-bundles curvature

Example of a real orientable $2n$-plane bundle without complex structure via non-trivial odd Stiefel-Whitney class

algebraic-topology vector-bundles characteristic-classes

The Pullback Bundle is an Embedded Submanifold of its Parent Space

differential-geometry vector-bundles smooth-manifolds

Understanding the trivialisation of a normal bundle

algebraic-topology vector-bundles fiber-bundles

Total space of a finite rank locally free sheaf, Vakil's 17.1.4 & 17.1.G

algebraic-geometry sheaf-theory vector-bundles schemes

Normal Bundle is Trivial

differential-geometry manifolds vector-bundles

Tangent bundle : is a manifold

manifolds vector-bundles

Does Hodge-star commute with metric connections?

differential-geometry riemannian-geometry vector-bundles connections

Are vector bundles isomorphic when their transition functions are homotopic?

manifolds vector-bundles

Covariant derivative of vector bundle map $\Psi:\xi\rightarrow \eta$

differential-geometry vector-bundles

Isomorphism class of vector bundle over $\mathbb S^1$.

algebraic-topology differential-topology vector-bundles

Nonisomorphic vector bundles with diffeomorphic total spaces

algebraic-topology differential-topology vector-bundles