{"paper_id":"2c2a4bc0-67d9-42e0-8d9d-0dc870778587","body_text":"Constructive Differential Algebraic Framework for Differential Topology: A Comprehensive Treatment with Certified Computations | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed.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 Constructive Differential Algebraic Framework for Differential Topology: A Comprehensive Treatment with Certified Computations Author : shifa liu 0009-0003-6570-2812 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176176529.93413941/v1 154 views 115 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract 本文建立了一个全面的微分拓扑建设微分代数框架，扩展了先前为外微分方程和偏微分方程开发的方法论。我们定义了微分拓扑代数闭包 K DT，这是一种通过递归附加过程构建的微分闭合结构，该过程结合了几何偏微分方程的解、建设性定义的调和形式、特征类和具有认证误差边界的拓扑不变量。在这个闭包中，我们证明了微分拓扑中基本问题的解决方案——包括谐波形式的构造、特征类代表和特殊几何结构，具有显式收敛率和误差估计的统一建设性表示。该框架严格解决了将局部坐标描述与全局拓扑约束相结合的挑战，同时保留了微分拓扑固有的几何和代数结构。我们提供详细的建设性证明和完整的误差分析，为具有严格边界的几何对象推导显式表达式，并在流形上适当的索博列夫空间中建立收敛标准。 Supplementary Material File (differential_topology.pdf) Download 428.41 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 constructive mathemac differential algebraic closure differential topology discrete exterior calculus harmonic forms hodge theory Authors Affiliations shifa liu 0009-0003-6570-2812 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 154 views 115 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation shifa liu. Constructive Differential Algebraic Framework for Differential Topology: A Comprehensive Treatment with Certified Computations. Authorea . 29 October 2025. DOI: https://doi.org/10.22541/au.176176529.93413941/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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