A structure theorem for homology 4-manifolds with g2 ≤ 5

IF 1 3区数学 Q3 MATHEMATICS, APPLIED Advances in Applied Mathematics Pub Date : 2024-04-24 DOI:10.1016/j.aam.2024.102705

Biplab Basak, Sourav Sarkar

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Abstract

Numerous structural findings of homology manifolds have been derived in various ways in relation to $g_{2}$ -values. The homology 4-manifolds with $g_{2} \leq 5$ are characterized combinatorially in this article. It is well-known that all homology 4-manifolds for $g_{2} \leq 2$ are polytopal spheres. We demonstrate that homology 4-manifolds with $g_{2} \leq 5$ are triangulated spheres and are derived from triangulated 4-spheres with $g_{2} \leq 2$ by a series of connected sum, bistellar 1- and 2-moves, edge contraction, edge expansion, and edge flipping operations. We establish that the above inequality is optimally attainable, i.e., it cannot be extended to $g_{2} = 6$ .

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g2 ≤ 5 的同构 4 维网格的结构定理

关于 g2 值，人们以各种方式得出了许多同构流形的结构结论。本文对 g2≤5 的同调 4-漫流形进行了组合描述。众所周知，g2≤2的所有同构4-manifolds都是多拓扑球。我们证明了 g2≤5 的同调 4-manifolds（同调 4-manifolds）是三角球，并且是通过一系列连通和、双星 1 和 2 移动、边收缩、边扩展和边翻转操作从 g2≤2 的三角 4-manifolds（同调 4-manifolds）派生出来的。我们确定上述不等式是最优的，即不能扩展到 g2=6。

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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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.

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A structure theorem for homology 4-manifolds with g2 ≤ 5

Abstract

A structure theorem for homology 4-manifolds with g2 ≤ 5