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arXiv · 2503.18490

Spheres and balls as independence complexes

Susan M. Cooper·Sara Faridi·Thiago Holleben·Lisa Nicklasson·Adam Van Tuyl
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Abstract

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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Susan M. Cooper, Sara Faridi, Thiago Holleben, Lisa Nicklasson, Adam Van Tuyl. 2025-03-24. Spheres and balls as independence complexes. https://doi.org/10.1215/00192082-12469402

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