1978
DOI: 10.1090/s0002-9947-1978-0492298-1
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3-pseudomanifolds with preassigned links

Abstract: Abstract. A 3-pseudomanifold is a finite connected simplicial 3-complex % such that every triangle in % belongs to precisely two 3-simplices of %, the link of every edge in % is a circuit, and the link of every vertex in % is a closed 2-manifold. It is proved that for every finite set 2 of closed 2-manifolds, there exists a 3-pseudomanifold % such that the link of every vertex in % is homeomorphic to some S e 2, and every S & 2 is homeomorphic to the link of some vertex in %.

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Cited by 10 publications
(4 citation statements)
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“…First consider the case when there exists a vertex w such that deg L (w) = 5. Let lk L (w)(= lk M (uw)) = C 5 (1,2,3,4,5).…”
Section: Proofsmentioning
confidence: 99%
See 1 more Smart Citation
“…First consider the case when there exists a vertex w such that deg L (w) = 5. Let lk L (w)(= lk M (uw)) = C 5 (1,2,3,4,5).…”
Section: Proofsmentioning
confidence: 99%
“…[13]). In [2], Altshuler has constructed another 8-vertex normal 3-pseudomanifold (namely, N 5 in Example 4). In [14], Lutz has shown that there exist exactly three 8-vertex normal 3-pseudomanifolds which are not combinatorial 3-manifolds (namely, N The topological properties of these normal 3-pseudomanifolds are given in Section 3.…”
Section: Introductionmentioning
confidence: 99%
“…. , j(m)) be a cycle which induces a diagonal-free circuit C in the diagram D of G. If the product S j (1)…”
Section: Complex Reflexion Groupsmentioning
confidence: 99%
“…Before we move on, note that the dual of the polytope 3 T 4 s = {{6, 3} s , {3, 3}} (with s = (1, 1), (2, 0)) is actually a 3-dimensional simplicial complex whose vertex links are isomorphic to the toroidal polyhedron {3, 6} s . A general result due to Altshuler [1] says that, given a finite set of abstract polyhedra which are simplicial 2-complexes, there always exists a finite 3-dimensional simplicial complex whose vertex links belong to the set (with each polyhedron in the set actually occurring as a link). This complex will be an abstract 4-polytope, but will generally not be regular.…”
Section: The Basic Enumeration Techniquementioning
confidence: 99%