Poincaré conjecture: A problem solved after a century of new ideas and continued work

IF 0.4 Q3 HISTORY & PHILOSOPHY OF SCIENCE
María Teresa Lozano Imízcoz
{"title":"Poincaré conjecture: A problem solved after a century of new ideas and continued work","authors":"María Teresa Lozano Imízcoz","doi":"10.7203/METODE.0.9265","DOIUrl":null,"url":null,"abstract":"The Poincare conjecture is a topological problem established in 1904 by the French mathematician Henri Poincare. It characterises three-dimensional spheres in a very simple way. It uses only the first invariant of algebraic topology – the fundamental group – which was also defined and studied by Poincare. The conjecture implies that if a space does not have essential holes, then it is a sphere. This problem was directly solved between 2002 and 2003 by Grigori Perelman, and as a consequence of his demonstration of the Thurston geometrisation conjecture, which culminated in the path proposed by Richard Hamilton.","PeriodicalId":41648,"journal":{"name":"Metode Science Studies Journal","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2017-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Metode Science Studies Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7203/METODE.0.9265","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
引用次数: 0

Abstract

The Poincare conjecture is a topological problem established in 1904 by the French mathematician Henri Poincare. It characterises three-dimensional spheres in a very simple way. It uses only the first invariant of algebraic topology – the fundamental group – which was also defined and studied by Poincare. The conjecture implies that if a space does not have essential holes, then it is a sphere. This problem was directly solved between 2002 and 2003 by Grigori Perelman, and as a consequence of his demonstration of the Thurston geometrisation conjecture, which culminated in the path proposed by Richard Hamilton.
庞加莱猜想:一个经过一个世纪的新思想和持续工作解决的问题
庞加莱猜想是法国数学家亨利·庞加莱于1904年提出的一个拓扑问题。它以一种非常简单的方式来表征三维球体。它只使用代数拓扑的第一个不变量——基群——这也是庞加莱定义和研究的。该猜想暗示,如果一个空间没有本质的空穴,那么它就是一个球体。Grigori Perelman在2002年至2003年间直接解决了这个问题,这是他对瑟斯顿几何化猜想的证明的结果,该猜想最终由Richard Hamilton提出。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Metode Science Studies Journal
Metode Science Studies Journal HISTORY & PHILOSOPHY OF SCIENCE-
CiteScore
0.80
自引率
0.00%
发文量
18
审稿时长
19 weeks
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信