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On neighbourly triangulations


Author: K. S. Sarkaria
Journal: Trans. Amer. Math. Soc. 277 (1983), 213-239
MSC: Primary 57Q15; Secondary 52A40
DOI: https://doi.org/10.1090/S0002-9947-1983-0690049-0
MathSciNet review: 690049
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Abstract: A simplicial complex is called $ d$-neighbourly if any $ d + 1$ vertices determine a $ d$-simplex. We give methods for constructing $ 1$-neighbourly triangulations of $ 3$- and $ 4$-manifolds; further we discuss some relationships between $ d$-neighbourly triangulations, chromatic numbers and the problem of finding upper and lower bounds on the number of simplices and locating the zeros of the characteristic polynomial of a triangulation. A triangulation of an orientable manifold is called order-orientable if there exists some ordering of the vertices which orients the manifold. We give necessary conditions for their existence; also we construct such triangulations on $ 3$-dimensional handlebodies and discuss the problem of recognising finite monotone subsets of an affine space by using these ideas.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0690049-0
Article copyright: © Copyright 1983 American Mathematical Society

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