一种轮系交错距离的性质

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-11-17 DOI:10.1112/blms.13187

François Petit, Pierre Schapira, Lukas Waas

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引用次数: 0

摘要

设X$ X$是具有距离满足适当性质的实解析流形，设k ${\bf k}$是一个域。见[Petit and Schapira]，《数学选集》，29(2023)，第2期。作者在X$ X$上的k ${\bf k}$ -模的派生范畴上构造了一个伪距离，推广了先前的构造[Kashiwara和Schapira， J. Appl.]。第一版。数学。Topol. 2(2018), 83-113。本文证明了X$ X$上具有紧支撑的两个可构造轴（或更一般地说，可构造轴直至无穷大）之间的距离为零，则这两个可构造轴是同构的，从而回答了Kashiwara和Schapira， J. appll的问题。第一版。数学。Topol. 2(2018), 83-113。我们还证明，由于Lesnick的存在，我们的结果暗示了一个类似的陈述。

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A property of the interleaving distance for sheaves

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A property of the interleaving distance for sheaves

Let $X$ be a real analytic manifold endowed with a distance satisfying suitable properties and let $k$ be a field. In [Petit and Schapira, Selecta Math. 29 (2023), no. 70, DOI 10.1007/s00029-023-00875-6], the authors construct a pseudo-distance on the derived category of sheaves of $k$ -modules on $X$ , generalizing a previous construction of [Kashiwara and Schapira, J. Appl. Comput. Math. Topol. 2 (2018), 83–113]. We prove here that if the distance between two constructible sheaves with compact support (or more generally, constructible sheaves up to infinity) on $X$ is zero, then these two sheaves are isomorphic, answering a question of [Kashiwara and Schapira, J. Appl. Comput. Math. Topol. 2 (2018), 83–113]. We also prove that our results imply a similar statement for finitely presentable persistence modules due to Lesnick.