Permuted difference cycles and triangulated sphere bundles
✍ Scribed by Wolfgang Kühnel; Gunter Lassmann
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 603 KB
- Volume
- 162
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
For any dimension d and any k = 1 .... ,d we construct a 2-neighborly triangulation of a d-manifold Mk a which is invariant under the action of the dihedral group D, on n = 2d-k(k + 3) --1 vertices. Mk n is the boundary of a (d + 1)-manifold Mdk+l with the same properties. Special cases in this family have been observed before: M~ is the boundary of a (d + 1)-simplex, ~t~_+] is an orientable or nonorientable 1-handle depending on the parity of d, M~ is a d-dimensional torus. Topologically, Mk d (or j~d+ 1) is the total space of a sphere bundle (or disc bundle) over a (d -k)-dimensional torus. The construction of the triangulation itself is purely combinatorial. It is based on permutations of certain difference cycles encoding all the information about the triangulation in d (or d + l) integers.