Spheres and balls as independence complexes
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913754189398016 |
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| author | Cooper, Susan M. Faridi, Sara Holleben, Thiago Nicklasson, Lisa Van Tuyl, Adam |
| author_facet | Cooper, Susan M. Faridi, Sara Holleben, Thiago Nicklasson, Lisa Van Tuyl, Adam |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18490 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spheres and balls as independence complexes Cooper, Susan M. Faridi, Sara Holleben, Thiago Nicklasson, Lisa Van Tuyl, Adam Combinatorics Commutative Algebra 05E45, 13F55, 05C69 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. |
| title | Spheres and balls as independence complexes |
| topic | Combinatorics Commutative Algebra 05E45, 13F55, 05C69 |
| url | https://arxiv.org/abs/2503.18490 |