L(2,1)
Closed 3-manifold · lens spaceobject:M/lens-2-1
- Area
- Area 3 · Closed 3-manifolds
- True vertices
- 2
- π₁
- ⟨ 4 | 4 ⟩
- H₁
- ℤ/2ℤ
- Diagram
- Topology.jl · virtual-link examples, figure 10
Closed normal o-graph
canonical gauss code[[[-1,-2,2,1]],[+,+]]- True vertices
- 2
- C1 · oriented circuits
- 1
- C2 · trivalent components
- 1
- C3 · method circuits
- 3
- Circuit lengths
- 8 · 3 · 1
π₁ presentation, unreduced
⟨ x₁, x₂, x₃, x₄ | x₁x₂⁻¹, x₂x₃⁻¹, x₄x₁x₁⁻¹, x₃x₂x₄⁻¹ ⟩
- Generators
- 4
- Relators
- 4
H₁ = ℤ/2ℤ
Abelianised from the presentation above.
- Free rank
- 0
- Torsion invariant factors
- 2
- Order
- 2
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 10
- Computation
- o-graph presentation pilot v1 · L(2,1)
Naming
Labels name the example. No independent identification of the object is claimed.