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arXiv · 2412.11354

Simplifications of finite spaces equipped with sheaves

Artem Malko
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Abstract

Following the classical results of Stong, we introduce a cohomological analogue of a core of a finite sheaved topological space and propose an algorithm for simplification in this category. In particular we generalize the notion of beat vertices and show that if a vertex of a sheaved space has topologically acyclic downset (with trivial coefficients), then its removal preserves the sheaf cohomology.

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Artem Malko. 2024-12-16. Simplifications of finite spaces equipped with sheaves. https://arxiv.org/abs/2412.11354

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