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gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:basisFor
|
gptkb:topology
|
|
gptkbp:canBe
|
musical composition
smooth
algebraic
real
holomorphic
|
|
gptkbp:class
|
gptkb:K-theory
gptkb:characteristic_classes
|
|
gptkbp:example
|
gptkb:Hopf_bundle
gptkb:Möbius_bundle
gptkb:tautological_bundle
tangent bundle
normal bundle
trivial bundle
|
|
gptkbp:fiberContent
|
gptkb:Vector
|
|
gptkbp:field
|
gptkb:algebraic_geometry
gptkb:mathematics
gptkb:topology
differential geometry
|
|
gptkbp:has_structure_group
|
gptkb:general_linear_group
|
|
gptkbp:has_transition_functions
|
gptkb:GL(n,_F)
|
|
gptkbp:hasSection
|
vector field
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
vector bundles
|
|
gptkbp:importantFor
|
gptkb:Riemann–Roch_theorem
gptkb:Atiyah–Singer_index_theorem
gptkb:algebraic_K-theory
gptkb:Chern_classes
gptkb:complex_cobordism
index theory
moduli spaces
sheaf theory
vector bundle cohomology
vector bundle connections
vector bundle curvature
vector bundle morphisms
vector field theory
|
|
gptkbp:introduced
|
mathematicians in the 20th century
|
|
gptkbp:rank
|
dimension of the fiber
|
|
gptkbp:relatedTo
|
principal bundles
line bundles
cotangent bundles
tangent bundles
|
|
gptkbp:type
|
gptkb:fiber
|
|
gptkbp:used_in
|
gptkb:gauge_theory
gptkb:theoretical_physics
gptkb:topology
complex geometry
|
|
gptkbp:bfsParent
|
gptkb:k-theory
|
|
gptkbp:bfsLayer
|
5
|