cohomological invariant
C58003
concept
A cohomological invariant is a rule that assigns to each object in a given class (such as algebraic varieties, groups, or topological spaces) an element of a cohomology group in a way that is functorial and captures structural or classification information about those objects.
All labels observed (6)
| Label | Occurrences |
|---|---|
| cohomological invariant canonical | 2 |
| cohomology operation | 2 |
| birational invariant (for smooth projective varieties over a field) | 1 |
| cohomological construction | 1 |
| cohomological refinement | 1 |
| secondary characteristic class | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: cohomological invariant
Generated description
A cohomological invariant is a rule that assigns to each object in a given class (such as algebraic varieties, groups, or topological spaces) an element of a cohomology group in a way that is functorial and captures structural or classification information about those objects.
Instances (8)
| Instance | Via concept surface |
|---|---|
| Herbrand quotient | — |
| Shafarevich group of a torus | — |
|
Chern–Simons forms
surface form:
Chern–Simons form
|
secondary characteristic class |
| Picard group | birational invariant (for smooth projective varieties over a field) |
| Beilinson regulator | cohomological construction |
| Steenrod operations | cohomology operation |
| Bockstein homomorphism | cohomology operation |
| Cheeger–Simons differential characters | cohomological refinement |