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))

- the base surface of the fibration
is specified
- 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

- for lens spaces, the value is always realized using

Page last updated on November 18, 2004