广义位形空间的同调稳定性和密度

IF 2 1区 数学
Q. Ho
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引用次数: 6

摘要

证明了截断多项式代数中系数格式的分解同调可以计算其广义位形空间的上同调。利用交换代数与李代数之间的Koszul对偶性,得到了李代数上同调的新表达式。因此,我们得到了处理广义位形空间的同调稳定性、同调密度和算术密度的统一的和概念性的方法。我们的结果对法布-沃尔夫森-伍德作品中出现的巧合进行了分类、概括,实际上提供了一种概念性的理解。我们对稳定同伦密度的计算也产生了理性同伦类型,回答了Vakil—Wood提出的问题。我们的方法取决于对上同源Chevalley配合物的同源稳定性的研究,这是一个独立的兴趣。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Homological stability and densities of generalized configuration spaces
We prove that the factorization homologies of a scheme with coefficients in truncated polynomial algebras compute the cohomologies of its generalized configuration spaces. Using Koszul duality between commutative algebras and Lie algebras, we obtain new expressions for the cohomologies of the latter. As a consequence, we obtain a uniform and conceptual approach for treating homological stability, homological densities, and arithmetic densities of generalized configuration spaces. Our results categorify, generalize, and in fact provide a conceptual understanding of the coincidences appearing in the work of Farb--Wolfson--Wood. Our computation of the stable homological densities also yields rational homotopy types, answering a question posed by Vakil--Wood. Our approach hinges on the study of homological stability of cohomological Chevalley complexes, which is of independent interest.
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来源期刊
Geometry & Topology
Geometry & Topology 数学-数学
自引率
5.00%
发文量
34
期刊介绍: Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.
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