Cheeger–Simons differential characters
E921617
Cheeger–Simons differential characters are geometric invariants that refine ordinary cohomology by incorporating both integral cohomology classes and differential form data, providing a model for differential cohomology theories.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
cohomological refinement
ⓘ
differential cohomology theory ⓘ geometric invariant ⓘ |
| alternativeModelTo | smooth Deligne cohomology NERFINISHED ⓘ |
| captures |
secondary characteristic classes
ⓘ
topological and geometric data simultaneously ⓘ |
| characterizedBy | homomorphisms from smooth cycles to R/Z ⓘ |
| compatibleWith |
de Rham isomorphism
NERFINISHED
ⓘ
integral period conditions ⓘ |
| definedOn | smooth manifolds ⓘ |
| degree | integer-graded ⓘ |
| encodes |
curvature forms
ⓘ
differential form data ⓘ holonomy information ⓘ integral cohomology classes ⓘ |
| field |
algebraic topology
ⓘ
differential geometry ⓘ global analysis ⓘ |
| fitsInto | exact sequence relating forms and integral cohomology ⓘ |
| generalizes |
line bundles with connection
ⓘ
principal bundles with connection ⓘ |
| hasApplicationIn |
anomaly theory
ⓘ
topological phases of gauge fields ⓘ |
| hasCurvatureMapTo | closed differential forms with integral periods ⓘ |
| hasStructure |
abelian group
ⓘ
graded group ⓘ |
| introducedIn | 1970s ⓘ |
| namedAfter |
James Simons
NERFINISHED
ⓘ
Jeff Cheeger NERFINISHED ⓘ |
| providesModelFor | differential cohomology ⓘ |
| refines |
de Rham cohomology
NERFINISHED
ⓘ
integral cohomology ⓘ singular cohomology ⓘ |
| relatedTo |
Chern–Simons invariants
NERFINISHED
ⓘ
Chern–Weil theory NERFINISHED ⓘ Deligne cohomology NERFINISHED ⓘ characteristic classes ⓘ |
| targetGroup | R/Z ⓘ |
| usedIn |
gauge theory
ⓘ
index theory ⓘ quantum field theory NERFINISHED ⓘ string theory NERFINISHED ⓘ |
| usedToDefine | differential refinements of characteristic classes ⓘ |
| usedToDescribe |
flux quantization conditions
ⓘ
holonomy of connections ⓘ |
| uses |
smooth differential forms
ⓘ
smooth singular chains ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.