hasUniversalCover
P70392
predicate
Indicates that one mathematical space serves as the universal covering space of another, mapping onto it via a covering map that is simply connected and covers all its loops.
All labels observed (4)
| Label | Occurrences |
|---|---|
| isUniversalCoverOf | 6 |
| hasUniversalCover canonical | 4 |
| universalCover | 3 |
| hasCoveringMapFrom | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: hasUniversalCover
Generated description
Indicates that one mathematical space serves as the universal covering space of another, mapping onto it via a covering map that is simply connected and covers all its loops.
Sample triples (14)
| Subject | Object |
|---|---|
| AdS isometry group SO(2,d) | Spin(2,d) ⓘ |
|
SO(3)
linked to:
rotation group SO(3)
|
SU(2)
via predicate surface "universalCover"
ⓘ
linked to:
rotation group SU(2)
|
|
SO(3)
linked to:
rotation group SO(3)
|
unit quaternions via predicate surface "hasCoveringMapFrom" ⓘ |
| SL(2,C) |
SO^+(3,1)
via predicate surface "isUniversalCoverOf"
ⓘ
linked to:
Lorentz group
|
|
SU(2)
linked to:
rotation group SU(2)
|
SO(3) via predicate surface "isUniversalCoverOf" NERFINISHED ⓘ |
| SO(2,d-1) | Spin(2,d-1) ⓘ |
| Spin(2,d) | SO(2,d)^{ ext{connected}} via predicate surface "isUniversalCoverOf" ⓘ |
|
SL(n,ℂ)
linked to:
special linear group SL(n,C)
|
itself for n ≥ 2 ⓘ |
| SL(2,ℤ) | PSL(2,ℤ) up to center via predicate surface "isUniversalCoverOf" ⓘ |
| PSL(2,ℝ) | universal covering group of SL(2,ℝ) via predicate surface "universalCover" ⓘ |
| SL(2,R) | universal covering group of SL(2,R) via predicate surface "universalCover" ⓘ |
| S^2 × R geometry | geometric S^2 × R 3-manifolds via predicate surface "isUniversalCoverOf" ⓘ |
|
PSL(2,ℂ)
linked to:
PSL(2,\mathbb{C})
|
SL(2,ℂ) NERFINISHED ⓘ |
| Teichmüller space | moduli space of Riemann surfaces via predicate surface "isUniversalCoverOf" NERFINISHED ⓘ |