Nov 3, 2023
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
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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
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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)
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
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Differential geometry is the study of curved surfaces, so I mean...