Observatory

Invariant observatory

One invariant read across the objects that carry it.

Object	π₁ Unreduced presentation from the raw edge data	H₁ Abelianisation of the presentation	MST · F_p[x]/(xᵖ) MST invariant over the truncated polynomial algebra	MST · U_q(sl₂) MST invariant over the quantum group	Kuperberg Kuperberg invariant	coverage
S³Area 3	⟨ x₁, x₂ \| x₁x₂⁻¹, x₂x₁x₁⁻¹ ⟩ Verified computation	0 Verified computation	— Uncomputed	— Uncomputed	— Uncomputed	2/5
L(2,1)Area 3	⟨ x₁, x₂, x₃, x₄ \| x₁x₂⁻¹, x₂x₃⁻¹, x₄x₁x₁⁻¹, x₃x₂x₄⁻¹ ⟩ Verified computation	ℤ/2ℤ Verified computation	— Uncomputed	— Uncomputed	— Uncomputed	2/5
L(3,1)Area 3	— Uncomputed	ℤ/3ℤ Computed	— Uncomputed	— Uncomputed	— Uncomputed	1/5
L(3,2)Area 3	— Uncomputed	ℤ/3ℤ Computed	— Uncomputed	— Uncomputed	— Uncomputed	1/5
S² × S¹Area 3	⟨ x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈ \| x₁x₂⁻¹, x₂x₃⁻¹, x₆x₇⁻¹, x₅x₆⁻¹, x₈x₁x₁⁻¹, x₇x₂x₈⁻¹, x₃x₆x₄⁻¹, x₄x₅x₅⁻¹ ⟩ Verified computation	ℤ Verified computation	— Uncomputed	— Uncomputed	— Uncomputed	2/5
PoincaréArea 3	— Uncomputed	0 Computed	— Uncomputed	— Uncomputed	— Uncomputed	1/5
UnknotArea 2	— Uncomputed	— Not applicable	— Not applicable	— Not applicable	— Uncomputed	0/2
TrefoilArea 2	— Uncomputed	— Not applicable	— Not applicable	— Not applicable	— Uncomputed	0/2
Hopf linkArea 2	— Uncomputed	— Not applicable	— Not applicable	— Not applicable	— Uncomputed	0/2
Borromean ringsArea 2	— Uncomputed	— Not applicable	— Not applicable	— Not applicable	— Uncomputed	0/2
Whitehead linkArea 2	— Uncomputed	— Not applicable	— Not applicable	— Not applicable	— Uncomputed	0/2