#vector bundle

[isomorphismes]

the cotangent bundle (differential forms) is the feminine side of calculus-on-manifolds; the tangent bundle (vector-fields) is the masculine side.

Shing-Shen Chern, via Richard Montgomery

[isomorphismes]

Chern classes are degeneracy loci. Vector bundles are equivalent iff their Chern polynomials are equal.

Ravi Vakil, introduction to jets from an algebraic-geometry point of view (1998)

[isomorphismes]

There is a one-to-one correspondence between vector bundles on a scheme and locally free sheaves on that scheme. • Line bundle=invertible sheaf • Vector bundle=locally free sheaf

David Eisenbud And Joe Harris, 3264 And all that

[inspirationhut]

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[jeksonjs]

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[ordinalitis]

Differential geometry is the study of curved surfaces, so I mean...