with non-empty boundary

We provide here the (computer-produced)
list of orientable finite-volume hyperbolic

3-manifolds *M* with non-empty
and compact totally geodesic boundary such that

the complexity of *M* (i.e.
the minimal number of tetrahedra in a triangulation of *M*)

is 3 or 4. We arrange the
*M*'s
according to their complexity and boundary, we

describe a geometric decomposition
into truncated hyperbolic tetrahedra obtained

by cutting the blocks of the Kojima
canonical decomposition, and we compute the

volume of *M*. In addition
we provide a presentation of the fundamental group of *M*

and we compute the first homology
group of *M*.

To understand the lists you should first know the format we use to describe a manifold.

The computer programs used to find the lists are described here.

Here come the lists:

Census of manifolds (as above) with complexity 3.

Census
of compact manifolds (as above) with complexity 4 and connected boundary
of genus 4.

(We have shown in
[30]
that the Kojima decomposition of such manifolds always consists of 4

truncated tetrahedra with all dihedral
angles Pi/12, so all the geometric invariants of the manifolds

in the list are the same: they
are only distinguished by the combinatorics of the gluings in

the Kojima decomposition.)

Census
of compact manifolds (as above) with complexity 4, connected boundary of
genus 3,

and canonical Kojima decomposition
into 4 tetrahedra.

Census
of compact manifolds (as above) with complexity 4, connected boundary of
genus 3,

and canonical Kojima decomposition
into 5 tetrahedra.

Census
of compact manifolds (as above) with complexity 4, connected boundary of
genus 3,

and canonical Kojima decomposition
into a single regular octahedron with all dihedral angles

equal to Pi/6. The triangulations
shown in this case are always obtained by cutting the octahedron

Census
of compact manifolds (as above) with complexity 4, connected boundary of
genus 2,

and canonical Kojima decomposition
into 4 tetrahedra.

Census
of compact manifolds (as above) with complexity 4, connected boundary of
genus 2,

and canonical Kojima decomposition
into 5 tetrahedra.

Census
of compact manifolds (as above) with complexity 4, connected boundary of
genus 2,

and canonical Kojima decomposition
into 6 tetrahedra.

Census
of compact manifolds (as above) with complexity 4, connected boundary of
genus 2,

and canonical Kojima decomposition
into 8 tetrahedra.

Census
of compact manifolds (as above) with complexity 4, connected boundary of
genus 2,

and canonical Kojima decomposition
into a single regular octahedron with all dihedral angles

equal to Pi/3. Again the
triangulations are obtained by cutting the octahedron.

Census
of compact manifolds (as above) with complexity 4, connected boundary of
genus 2,

and canonical Kojima decomposition
into a single non-regular octahedron. The octahedron

is geometrically the same for all
manifolds, and the triangulations are obtained by cutting it.

Census
of compact manifolds (as above) with complexity 4, connected boundary of
genus 2,

and canonical Kojima decomposition
into two pyramids with square basis. The pyramids

are geometrically the same for
all manifolds, and the triangulations are obtained by cutting them.

Census
of non-compact manifolds (as above) with complexity 4.

Page last updated on November 28, 2002