莫尔斯炮弹的光谱序列

IF 0.8 4区 数学 Q2 MATHEMATICS Homology Homotopy and Applications Pub Date : 2020-12-03 DOI:10.4310/hha.2022.v24.n2.a11
Jean-Yves Welschinger
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引用次数: 3

摘要

我们最近引入了有限单纯复形几何实现的tilings的概念,并将这些tilings与R.Forman的离散Morse理论联系起来,特别是当它们具有可壳的性质时,这是经典可壳复形所共有的性质。我们现在观察到,每一个这样的瓦片都支持一个颤动,当瓦片是可剥的时,这个颤动是非循环的,然后每一次剥都诱导两个光谱序列,这两个序列收敛到复合物的(共)同源性。他们的第一页是在瓷砖的关键瓷砖上的免费模块。
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Spectral sequences of a Morse shelling
We recently introduced a notion of tilings of the geometric realization of a finite simplicial complex and related those tilings to the discrete Morse theory of R. Forman, especially when they have the property to be shellable, a property shared by the classical shellable complexes. We now observe that every such tiling supports a quiver which is acyclic precisely when the tiling is shellable and then that every shelling induces two spectral sequences which converge to the (co)homology of the complex. Their first pages are free modules over the critical tiles of the tiling.
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
37
审稿时长
>12 weeks
期刊介绍: Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.
期刊最新文献
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