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

Lozano Imizcoz, María Teresa (Universidad de Zaragoza)

Resumen: The Poincaré conjecture is a topological problem established in 1904 by the French mathematician Henri Poincaré. 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 Poincaré. 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.

Idioma: Inglés

DOI: 10.7203/metode.8.9265

Año: 2018

Publicado en: Mètode (Valencia) 8 (2018), 83-91
ISSN: 1133-3987

Financiación: info:eu-repo/grantAgreement/ES/DGA/E15
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2013-45710-C2-1-P
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2016-76868-C2-2-P

Tipo y forma: Article (Published version)

Área (Departamento): Área Geometría y Topología (Dpto. Matemáticas)