S³
Closed 3-manifold · sphereobject:M/s3
- Area
- Area 3 · Closed 3-manifolds
- True vertices
- 1
- π₁
- ⟨ 2 | 2 ⟩
- H₁
- 0
- Diagram
- Topology.jl · virtual-link examples, figure 4
Closed normal o-graph
canonical gauss code[[[-1,1]],[+]]- True vertices
- 1
- C1 · oriented circuits
- 1
- C2 · trivalent components
- 1
- C3 · method circuits
- 2
- Circuit lengths
- 5 · 1
π₁ presentation, unreduced
⟨ x₁, x₂ | x₁x₂⁻¹, x₂x₁x₁⁻¹ ⟩
- Generators
- 2
- Relators
- 2
H₁ = 0
Abelianised from the presentation above.
- Free rank
- 0
- Torsion invariant factors
- none
- Order
- 1
Invariants
| π₁Unreduced presentation from the raw edge data | Verified computation |
| H₁Abelianisation of the presentation | Verified computation |
| MST · F_p[x]/(xᵖ)MST invariant over the truncated polynomial algebra | Uncomputed |
| MST · U_q(sl₂)MST invariant over the quantum group | Uncomputed |
| KuperbergKuperberg invariant | Uncomputed |
- Diagram
- Topology.jl · virtual-link examples, figure 4
- Computation
- o-graph presentation pilot v1 · S³
Naming
Labels name the example. No independent identification of the object is claimed.