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arXiv · 2406.18989

The generic anisotropy of strongly edge decomposable spheres

Feifei Fan
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Abstract

The generic anisotropy is an important property in the study of Stanley-Reisner rings of homology spheres, which was introduced by Papadakis and Petrotou. This property can be used to prove the strong Lefschetz property as well as McMullen's $g$-conjecture for homology spheres. It is conjectured that for an arbitrary field $\mathbb{F}$, any $\mathbb{F}$-homology sphere is generically anisotropic over $\mathbb{F}$. In this paper, we prove this conjecture for all strongly edge decomposable spheres.

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Feifei Fan. 2024-06-27. The generic anisotropy of strongly edge decomposable spheres. https://arxiv.org/abs/2406.18989

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