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The non-pure version of the simplex and the boundary of the simplex

We introduce the non-pure versions of simplicial balls and spheres with minimum number of vertices. These are a special type of non-homogeneous balls and spheres (NH-balls and NH-spheres) satisfying a minimality condition on the number of maximal simplices. The main result is that minimal NH-balls and NH-spheres are precisely the simplicial complexes whose iterated Alexander duals converge respectively to a simplex or the boundary of a simplex.

preprint2014arXivOpen access
Nicolas Ariel Capitelli
math.COmath.GT
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Nicolas Ariel Capitelli

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