{"title":"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","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":"{\"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}","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}
Poincaré conjecture: A problem solved after a century of new ideas and continued work
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.