Three-manifolds up to complexity 10

Classification of closed orientable irreducible 3-manifolds
having a triangulation with at most 10 tetrahedra.

You can see here the tables of the manifolds we have found in complexity 1 to 9.
For each complexity we list the manifolds according to their geometry and JSJ
decomposition, and we provide a summarizing table.  See below for important
conventions used in the tables, and here for the computer programs used to find the data.

- Complexity 1: tables

- Complexity 2: tables

- Complexity 3: tables

- Complexity 4: tables

- Complexity 5: tables

- Complexity 6: tables

- Complexity 7: tables

- Complexity 8: tables

- Complexity 9: tables

- Complexity 10: tables
(this census refers to the following list of small hyperbolic manifolds
not included in SnapPea's list, because they have very short geodesics)

Conventions used in the tables:
• the manifolds of complexity 0, i.e. the sphere, projective 3-space, and L(3,1), are not listed
• `elliptic' means `elliptic and not a lens space'
• when Seifert manifolds are involved
• the base surface of the fibration is specified either before the table or in the first line of the table
• D, S, A stand respectively for the disc, the Moebius strip, the annulus
• the parameters (p,q) of a fibre are the filling parameters, not the orbital parameters
• the additional twisting parameter b is equivalent to a fiber of type (1,b)
• for the twisted circle bundle over the Moebius strip we have always used
the alternative fibration (D,(2,1),(2,1))
• when non-trivial graph manifolds are involved, the gluing (or self-gluing) matrices
are expressed with respect to the homology bases described in [34]
• the `census' referred to for closed hyperbolic manifolds is a list of 144
Dehn surgeries on the chain link with 3 components, that we propose as the
candidate list of all smallest closed manifolds with volume < 1.96.
(It contains the 39 manifolds of the census of Callahan, Hildebrand, and Weeks
having volume < 1.96 and geodesics longer than 0.3).
• we have organized the tables in order to show which bricks are used to realize the exact
value of complexity of each manifold (see [34]), namely
• for lens spaces, the value is always realized using B2 and B3
• for all other Seifert spaces and graph manifolds, unless otherwise indicated,
the value is realized using B2, B3 and B4 (sometimes without B3)
• the only exceptions to the point just stated are the closed bricks C(i,j), E(k)
and some manifolds for which the brick B5 is employed
• the hyperbolic bricks are only used for the hyperbolic manifolds

Page last updated on November 18, 2004