S² × S¹
Closed 3-manifold · productobject:M/s2xs1
- Area
- Area 3 · Closed 3-manifolds
- True vertices
- 4
- π₁
- ⟨ 8 | 8 ⟩
- H₁
- ℤ
- Diagram
- Topology.jl · virtual-link examples, figure 14
Closed normal o-graph
canonical gauss code[[[-1,-2,3,4,-4,-3,2,1]],[+,+,+,+]]- True vertices
- 4
- C1 · oriented circuits
- 1
- C2 · trivalent components
- 1
- C3 · method circuits
- 5
- Circuit lengths
- 8 · 6 · 1 · 8 · 1
π₁ presentation, unreduced
⟨ x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈ | x₁x₂⁻¹, x₂x₃⁻¹, x₆x₇⁻¹, x₅x₆⁻¹, x₈x₁x₁⁻¹, x₇x₂x₈⁻¹, x₃x₆x₄⁻¹, x₄x₅x₅⁻¹ ⟩
- Generators
- 8
- Relators
- 8
H₁ = ℤ
Abelianised from the presentation above.
- Free rank
- 1
- Torsion invariant factors
- none
- Order
- ∞
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 14
- Computation
- o-graph presentation pilot v1 · S² × S¹
Naming
Labels name the example. No independent identification of the object is claimed.