Mathematics – Geometric Topology
Scientific paper
2007-09-10
Mathematics
Geometric Topology
27 pages, 2 figures
Scientific paper
We enumerate all spaces obtained by gluing in pairs the faces of the octahedron in an orientation-reversing fashion. Whenever such a gluing gives rise to non-manifold points, we remove small open neighbourhoods of these points, so we actually deal with three-dimensional manifolds with (possibly empty) boundary. There are 298 combinatorially inequivalent gluing patterns, and we show that they define 191 distinct manifolds, of which 132 are hyperbolic and 59 are not. All the 132 hyperbolic manifolds were already considered in different contexts by other authors, and we provide here their known ``names'' together with their main invariants. We also give the connected sum and JSJ decompositions for the 59 non-hyperbolic examples. Our arguments make use of tools coming from hyperbolic geometry, together with quantum invariants and more classical techniques based on essential surfaces. Many (but not all) proofs were carried out by computer, but they do not involve issues of numerical accuracy.
Heard Damian
Pervova Ekaterina
Petronio Carlo
No associations
LandOfFree
The 191 orientable octahedral manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The 191 orientable octahedral manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The 191 orientable octahedral manifolds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-656429