Atlas of 3-Manifolds

Getting started Search Manifold recognizer Example

ε - invariant

polinomial of ε

t(M) = ε +

estimates of its real value

≤ t(M) ≤

Geometry

E³

S³

S² x R

H² x R

SL₂R

Nil

Sol

H³ Volume ≤ V(M) ≤

Nongeometric

Complexity

exact value of the complexity

c(M)=

estimates of the complexity

≤ c(M) ≤

Homology group

Number of summands in torsion subgroup
Tor(H₁) =

Torsion-free rank of H₁ =

H₁ = 0

Heegaard genus

g(M) =

Stalling manifolds

Search stallings manifold.

Seifert manifolds

Euler characteristic of base:	χ(F)=
Number of exceptional fibers:	n =
Orientation of F:

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Other invariants
	ε - invariant
	geometry
	Heegaard genus
	Homology group
	Spine code

Mark the row "Complexity".
Next

Mark "upper and lower bounds".
Choose c(M) berween 4 and 8. Next

Mark the row "Homology group" Next

Choose Tor(H₁)=2,
and then choose Torsion-free rank of H₁=0.
Then replace two zeros by 2 and 4. Next

Click "search" button below. Next