热带poincarcarcars对偶空间

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2021-12-07 DOI:10.1515/advgeom-2023-0017

E. Aksnes

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引用次数: 2

摘要

有理平衡多面体扇的热带基类推导出热带上同与热带Borel-Moore同的盖积。当所有这些帽积都是同构时，这个扇形就是一个热带庞卡罗对偶空间。如果所有面的星形也都是这样的空间，如拟阵的扇形，则扇形被称为局部热带庞卡罗对偶空间。本文首先给出了扇形是热带庞卡罗对偶空间的若干必要条件，并给出了扇形在1维上的分类。其次，我们证明了所有维度大于零的面和一个消失条件的星的热带庞卡罗莱对偶性暗示了扇形的热带庞卡罗莱对偶性。这就为扇形成为一个局部的热带庞卡罗双重性空间提供了必要和充分的条件。最后，我们利用这些扇形来证明某些抽象的平衡多面体空间满足热带庞卡罗对偶性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Tropical Poincaré duality spaces

Abstract The tropical fundamental class of a rational balanced polyhedral fan induces cap products between tropical cohomology and tropical Borel–Moore homology. When all these cap products are isomorphisms, the fan is said to be a tropical Poincaré duality space. If all the stars of faces also are such spaces, such as for fans of matroids, the fan is called a local tropical Poincaré duality space. In this article, we first give some necessary conditions for fans to be tropical Poincaré duality spaces and a classification in dimension one. Next, we prove that tropical Poincaré duality for the stars of all faces of dimension greater than zero and a vanishing condition implies tropical Poincaré duality of the fan. This leads to necessary and sufficient conditions for a fan to be a local tropical Poincaré duality space. Finally, we use such fans to show that certain abstract balanced polyhedral spaces satisfy tropical Poincaré duality.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.