geometric invariant
C10588
concept
A geometric invariant is a property of a geometric object that remains unchanged under a specified group of transformations, such as rotations, translations, or more general symmetries.
All labels observed (27)
| Label | Occurrences |
|---|---|
| algebraic invariant | 9 |
| characteristic class | 6 |
| geometric concept | 3 |
| geometric invariant canonical | 3 |
| gauge-theoretic invariant | 2 |
| invariant in geometric group theory | 2 |
| invariant of dynamical systems | 2 |
| numerical invariant | 2 |
| symplectic invariant | 2 |
| Laurent polynomial–valued invariant | 1 |
| Lie algebra invariant | 1 |
| complex-analytic invariant | 1 |
| curvature notion | 1 |
| holomorphic invariant | 1 |
| invariant in algebraic geometry | 1 |
| invariant in complex geometry | 1 |
| invariant in the geometry of numbers | 1 |
| invariant metric in complex analysis | 1 |
| metric geometry concept | 1 |
| object in spectral geometry | 1 |
| polyhedral invariant | 1 |
| projective invariant | 1 |
| singularity invariant | 1 |
| smooth structure invariant | 1 |
| spectral invariant | 1 |
| symmetry index | 1 |
| translation-invariant measure | 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: geometric invariant
Generated description
A geometric invariant is a property of a geometric object that remains unchanged under a specified group of transformations, such as rotations, translations, or more general symmetries.
Instances (42)
| Instance | Via concept surface |
|---|---|
| Jones polynomial | Laurent polynomial–valued invariant |
| Lyapunov exponents | invariant of dynamical systems |
|
Menger
surface form:
Menger curvature
|
geometric concept |
| Menger curvature | geometric concept |
| Castelnuovo–Mumford regularity | algebraic invariant |
| Chern classes | characteristic class |
| Clebsch–Aronhold invariants | algebraic invariant |
| Dehn invariant | — |
| Dehn function | invariant in geometric group theory |
| Milnor number | singularity invariant |
| Gelfand–Kirillov dimension | algebraic invariant |
| Fitting ideal | algebraic invariant |
| Lebesgue measure | translation-invariant measure |
| Plücker coordinates | projective invariant |
| Chern character | characteristic class |
| Todd class | characteristic class |
| Laplacian spectrum | spectral invariant |
| Banach–Mazur distance | numerical invariant |
| Dyson index β | symmetry index |
| Hermite constant | invariant in the geometry of numbers |
| Donaldson invariants | gauge-theoretic invariant |
| Kobayashi metric | invariant metric in complex analysis |
| Lempert function on convex domains | complex-analytic invariant |
| Cartan–Killing form | Lie algebra invariant |
|
Dolbeault cohomology classes
surface form:
Dolbeault cohomology class
|
invariant in complex geometry |
| Ricci scalar | — |
| Euler class | characteristic class |
| Arf invariant | algebraic invariant |
| Lusternik–Schnirelmann category | numerical invariant |
| Lyapunov dimension | invariant of dynamical systems |
| Hilbert polynomial | algebraic invariant |
| Stiefel–Whitney classes | characteristic class |
| Picard group | algebraic invariant |
| Maslov index | symplectic invariant |
| Seiberg–Witten invariants | gauge-theoretic invariant |
| Liouville measure | symplectic invariant |
| Hurwitz numbers | algebraic invariant |
| Godbillon–Vey invariant | characteristic class |
| Miquel circle | geometric concept |
| Chow groups | algebraic invariant |
| Cheeger–Simons differential characters | — |
|
Whitehead groups
surface form:
Whitehead group
|
invariant in geometric group theory |