Observations from the 8-Tetrahedron Nonorientable Census

نویسنده

  • Benjamin A. Burton
چکیده

Through computer enumeration with the aid of topological results, we catalogue all 18 closed nonorientable P-irreducible 3-manifolds that can be formed from at most eight tetrahedra. In addition we give an overview as to how the 100 resulting minimal triangulations are constructed. Observations and conjectures are drawn from the census data, and future potential for the nonorientable census is discussed. Some preliminary nine-tetrahedron results are also included.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Duplicate Pair in the SnapPea Census

We identify a duplicate pair in the well-known Callahan-HildebrandWeeks census of cusped finite-volume hyperbolic 3-manifolds. Specifically, the six-tetrahedron non-orientable manifolds x101 and x103 are homeomorphic.

متن کامل

2 2 D ec 1 99 8 A Note on the Gauss Map of Complete Nonorientable Minimal Surfaces

We construct complete nonorientable minimal surfaces whose Gauss map omits two points of RP 2 . This result proves that Fujimoto’s theorem is sharp in nonorientable case.

متن کامل

Enumeration of non-orientable 3-manifolds using face pairing graphs and union-find

Drawing together techniques from combinatorics and computer science, we improve the census algorithm for enumerating closed minimal P-irreducible 3-manifold triangulations. In particular, new constraints are proven for face pairing graphs, and pruning techniques are improved using a modification of the union-find algorithm. Using these results we catalogue all 136 closed nonorientable P-irreduc...

متن کامل

0 M ay 2 00 7 Nonorientable 3 - manifolds admitting coloured triangulations with at most 30 tetrahedra ∗

We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid nonbipartite crystallizations up to 30 vertices. 2000 Mathematics Subject Classification: 57Q15, 57M15, 57N10.

متن کامل

Computing Arithmetic Invariants of 3-Manifolds

This paper describes “Snap”, a computer program for computing arithmetic invariants of hyperbolic 3-manifolds. Snap is based on Jeff Weeks’s program “SnapPea” [41] and the number theory package “Pari” [5]. SnapPea computes the hyperbolic structure on a finite volume hyperbolic 3-manifold numerically (from its topology) and uses it to compute much geometric information about the manifold. Snap’s...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Experimental Mathematics

دوره 16  شماره 

صفحات  -

تاریخ انتشار 2007