The non-pure version of the simplex and the boundary of the simplex
Copyright policy )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.
9 pages
- University of Buenos Aires Argentina
- National Scientific and Technical Research Council Argentina
combinatorial manifold, Polyhedral manifolds, Combinatorial aspects of simplicial complexes, Geometric Topology (math.GT), Alexander dual, 55M05, 52B70, 57Q99, Mathematics - Geometric Topology, General topology of complexes, Simplicial Complex, FOS: Mathematics, https://purl.org/becyt/ford/1.1, simplicial complex, Mathematics - Combinatorics, Combinatorial Manifolds, Alexander Dual, Combinatorics (math.CO), https://purl.org/becyt/ford/1
combinatorial manifold, Polyhedral manifolds, Combinatorial aspects of simplicial complexes, Geometric Topology (math.GT), Alexander dual, 55M05, 52B70, 57Q99, Mathematics - Geometric Topology, General topology of complexes, Simplicial Complex, FOS: Mathematics, https://purl.org/becyt/ford/1.1, simplicial complex, Mathematics - Combinatorics, Combinatorial Manifolds, Alexander Dual, Combinatorics (math.CO), https://purl.org/becyt/ford/1
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