A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.

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### Homology of Hirzebruch surfaces

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### The heat kernel in Hermitian bundles over Riemannian manifolds

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### Vector Bundle Structure of Conformal Block Bundle

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### Dual of a stable locally free subsheaf is a locally free quotient sheaf

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### Motivation for classifying vector bundles

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### Harder-Narasimhan over arbitrary coefficients

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### First cohomology class of co-sphere bundle of $\mathbb{C}P^n$ [closed]

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### What would be the simplest analog of Langlands in algebraic topology?

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### different reductions for a vector bundle

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### Sections of vector bundles with exactly one zero

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### Confusion in known result about Moduli space of vector bundle of rank 2 degree 0 vector bundles over smooth curve of genus 2

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### Thom space, homotopy group and cohomology group

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### Fourth obstruction, Pontryagin and Euler class

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### When is the Chern class of a principal $G$-bundle same to the Chern class of the associated complex vector bundle?

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### Harder Narasimhan filtration for the endomorphism bundle

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### Gluing locally defined continous functions over complex domain

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### semistability of an extension of bundles

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### About universal Ext space

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### Stable torsion free sheaf on smooth projective surface

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### Existence of sections of a fibre bundle which are covariantly constant along certain directions

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### When is the moduli of generalized parabolic bundles with fixed determinant smooth?

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### Set of sections whose zeroes avoid a given divisor is (Zariski) dense?

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### Restriction of vector bundles

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### Singularities of quotient of a vector bundle by a lattice

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### Extension of a rational section of a projective bundle

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### Do $\mathbb{HP}^2\#\overline{\mathbb{HP}^2}$ and $\mathbb{OP}^2\#\overline{\mathbb{OP}^2}$ arise as sphere bundles over spheres?

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### Elements of graded algebra associated with the algebra of differential operators as smooth sections

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### Connection 1-form of the frame bundle associated to a vector bundle with a connection

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### Extending vector bundles over a regular divisor in a regular affine scheme

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### Endomorphism of involution invariant vector bundles

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### Which object related to families of algebraic varieties over a scheme $ S $ corresponds to the tensor product of vector bundles?

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### Endomorphism sheaves of vector bundles

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### Exercise in the book “Lectures on Kähler geometry”

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### Existence of very Stable bundle on a compact Riemann surface

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### Positive cones in K-groups

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### semistability of parabolic bundles

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### Principal $G$-bundles on affine toric varieties

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### Interesting examples of vector bundles on hyperkahler varieties

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### Extend a gauge transformation

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### Vector bundles on space of germs

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### Role of stably free modules in algebraic geometry

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### Tangent space and a subset of a tame Lie group

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### A refined comparison of isomorphic vector bundles on a compact space

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### Holomorphic line bundles on $\mathbb{P}^1$ from gluing data

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### Isomorphism classes of line bundles with connections

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### Vector fields on quasi-spheres

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### Spinor bundle tensored with certain line bundle gives the dual spinor bundle

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### First Chern class of a specific line bundle

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### On sections into Banach bundles over a compact manifold

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