论文标题
大规模的多参数持续模块
Multiparameter persistence modules in the large scale
论文作者
论文摘要
带有$ M $离散参数的持久模块是由POSET $ \ MATHBB {N}^M $索引的向量空间的图。如果我们只对这样的图表的大规模行为感兴趣，那么如果它们同意在``可忽视''地区之外，我们就可以考虑两个图表。在$ 2 $维情况下，我们将不可分解的图表分类为有限支持的图。在较高的维度中，我们部分将不可塑性的图表分类为适当的有限图，并表明完整的分类问题是狂野的。
A persistence module with $m$ discrete parameters is a diagram of vector spaces indexed by the poset $\mathbb{N}^m$. If we are only interested in the large scale behavior of such a diagram, then we can consider two diagrams equivalent if they agree outside of a ``negligeable'' region. In the $2$-dimensional case, we classify the indecomposable diagrams up to finitely supported diagrams. In higher dimension, we partially classify the indecomposable diagrams up to suitably finite diagrams, and show that the full classification problem is wild.
