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