Statements (33)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
complex vector bundles
|
| gptkbp:codomain |
second cohomology group
|
| gptkbp:field |
gptkb:algebraic_geometry
gptkb:topology differential geometry |
| gptkbp:generalizes |
gptkb:Euler_class_for_complex_line_bundles
|
| gptkbp:heldBy |
a topological invariant
the determinant of the transition functions of a line bundle additive under direct sum of bundles an element of H^2(X, Z) for a space X an invariant under bundle isomorphism the curvature form in Chern-Weil theory the degree of a line bundle over a Riemann surface the divisor class in algebraic geometry the first element in the sequence of Chern classes the obstruction to a line bundle being trivial an obstruction to the existence of nonvanishing sections zero for trivial bundle multiplicative under tensor product of line bundles the first Stiefel-Whitney class for real bundles modulo 2 |
| https://www.w3.org/2000/01/rdf-schema#label |
first Chern class
|
| gptkbp:namedAfter |
gptkb:Shiing-Shen_Chern
|
| gptkbp:notation |
c₁
|
| gptkbp:usedIn |
gptkb:Riemann-Roch_theorem
gptkb:characteristic_classes intersection theory algebraic cycles complex manifolds vector bundle theory classification of line bundles |
| gptkbp:bfsParent |
gptkb:Chern_classes
|
| gptkbp:bfsLayer |
6
|