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Spheres and balls as independence complexes

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arxiv 2503.18490 v1 pith:OSVS42FL submitted 2025-03-24 math.CO math.AC

Spheres and balls as independence complexes

classification math.CO math.AC
keywords complexesindependenceballsgraftinghomeomorphicidealsphereswhiskering
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The terms "whiskering", and more generally "grafting", refer to adding generators to any monomial ideal to make the resulting ideal Cohen-Macaulay. We investigate the independence complexes of simplicial complexes that are constructed through a whiskering or grafting process, and we show that these independence complexes are (generalized) Bier balls. More specifically, the independence complexes are either homeomorphic to a ball or a sphere. In a related direction, we classify when the independence complexes of very well-covered graphs are homeomorphic to balls or spheres.

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