Unified Analytic Representation of Geometric Topological Invariants via Geometric Topological Algebraic Closure

Unified Analytic Representation of Geometric Topological Invariants via Geometric Topological Algebraic Closure | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 29 October 2025 V1 Latest version Share on Unified Analytic Representation of Geometric Topological Invariants via Geometric Topological Algebraic Closure Authors : Dongqi Liu 0009-0006-4018-9292 and shifa liu 0009-0003-6570-2812 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176176530.01094563/v1 219 views 114 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract 本文为获得几何拓扑不变量的显式解析表示建立了一个严谨而建设性的框架。我们引入了几何拓扑代数闭包 K geom ，它通过相邻拓扑不变量、几何结构（度量、连接、曲率）及其相关算子来扩展系数场。在这个闭包中，我们证明了关键的几何拓扑不变量——包括特征类、Seiberg-Witten 不变量、Reidemeister 扭转和 Gromov-Witten 不变量sadmit 统一了以下形式的显式表示：I（M） = M m=1 我们通过详细的收敛分析提供完整的建设性证明，从莫尔斯和手术理论中推导出组合系数的显式表达式，并提出详细的算法和复杂性分析以进行计算实现。对经典示例的广泛理论验证证明了与既定结果的一致性，同时提供了新的显式公式。这项工作通过证明显式解析解存在于适当扩展的几何拓扑代数闭包 K geom 中，与经典的非建构性结果相协调。 Supplementary Material File (geometic_topology1.pdf) Download 460.00 KB Information & Authors Information Version history V1 Version 1 29 October 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords characteristic classes combinatorial topology computational topology explicit representation geometric topology seiberg-witten invariants topological algebraic closure Authors Affiliations Dongqi Liu 0009-0006-4018-9292 View all articles by this author shifa liu 0009-0003-6570-2812 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 219 views 114 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Dongqi Liu, shifa liu. Unified Analytic Representation of Geometric Topological Invariants via Geometric Topological Algebraic Closure. Authorea . 29 October 2025. DOI: https://doi.org/10.22541/au.176176530.01094563/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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