fundamentalGroup
P78388
predicate
Indicates the relationship that assigns to a topological space its fundamental group, capturing how loops in the space can be continuously deformed into one another.
All labels observed (3)
| Label | Occurrences |
|---|---|
| fundamentalGroup canonical | 10 |
| fundamentalGroupOfCompactQuotient | 1 |
| fundamentalGroupProperty | 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: fundamentalGroup
Generated description
Indicates the relationship that assigns to a topological space its fundamental group, capturing how loops in the space can be continuously deformed into one another.
Sample triples (12)
| Subject | Object |
|---|---|
|
SO(3)
linked to:
rotation group SO(3)
|
ℤ₂ ⓘ |
| Riemann sphere | trivial group ⓘ |
|
SO(3)
linked to:
special orthogonal group SO(n)
|
ℤ/2ℤ ⓘ |
|
SO(n)
linked to:
special orthogonal group SO(n)
|
ℤ for n = 2 ⓘ |
|
SO(n)
linked to:
special orthogonal group SO(n)
|
ℤ/2ℤ for n ≥ 3 ⓘ |
|
SU(n)
linked to:
special unitary group SU(n)
|
trivial (for n ≥ 2) ⓘ |
|
GL(n,ℂ)
linked to:
general linear group GL(n,C)
|
ℤ ⓘ |
| PSL(2,ℝ) | ℤ ⓘ |
| SL(2,R) | Z ⓘ |
| S^2 × R geometry | extension of Z by finite group via predicate surface "fundamentalGroupOfCompactQuotient" ⓘ |
| 4-sphere S^4 | trivial group ⓘ |
|
Seifert fibered space
linked to:
Seifert fibered spaces
|
contains infinite cyclic normal subgroup generated by a regular fiber via predicate surface "fundamentalGroupProperty" ⓘ |