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Transactions of the American Mathematical Society

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$ 3$-pseudomanifolds with preassigned links

Author: Amos Altshuler
Journal: Trans. Amer. Math. Soc. 241 (1978), 213-237
MSC: Primary 57N10; Secondary 57Q05
MathSciNet review: 492298
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Abstract: A 3-pseudomanifold is a finite connected simplicial 3-complex $ \mathcal{K}$ such that every triangle in $ \mathcal{K}$ belongs to precisely two 3-simplices of $ \mathcal{K}$, the link of every edge in $ \mathcal{K}$ is a circuit, and the link of every vertex in $ \mathcal{K}$ is a closed 2-manifold. It is proved that for every finite set $ \sum $ of closed 2-manifolds, there exists a 3-pseudomanifold $ \mathcal{K}$ such that the link of every vertex in $ \mathcal{K}$ is homeomorphic to some $ S\, \in \,\sum $, and every $ S\, \in \,\sum $ is homeomorphic to the link of some vertex in $ \mathcal{K}$.

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Keywords: 3-pseudomanifold, simplicial complex, 2-manifold, 3-manifold, link, star, assembling, neighborly complex, f-vector, convex polytope, automorphism-group, finite field, projective transformation, nerve-graph, Gale-diagram
Article copyright: © Copyright 1978 American Mathematical Society

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