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.

Observed surface forms (2)

fundamentalGroupOfCompactQuotient ×1
fundamentalGroupProperty ×1

Sample triples (12)

Subject	Object
4-sphere S^4	trivial group ⓘ
general linear group GL(n,C) surface form: GL(n,ℂ)	ℤ ⓘ
PSL(2,ℝ)	ℤ ⓘ
Riemann sphere	trivial group ⓘ
SL(2,R)	Z ⓘ
special orthogonal group SO(n) surface form: SO(3)	ℤ/2ℤ ⓘ
rotation group SO(3) surface form: SO(3)	ℤ₂ ⓘ
special orthogonal group SO(n) surface form: SO(n)	ℤ for n = 2 ⓘ
special orthogonal group SO(n) surface form: SO(n)	ℤ/2ℤ for n ≥ 3 ⓘ
special unitary group SU(n) surface form: SU(n)	trivial (for n ≥ 2) ⓘ
S^2 × R geometry	extension of Z by finite group via predicate surface "fundamentalGroupOfCompactQuotient" ⓘ
Seifert fibered spaces surface form: Seifert fibered space	contains infinite cyclic normal subgroup generated by a regular fiber via predicate surface "fundamentalGroupProperty" ⓘ