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Sur Les Groupes Hyperboliques D'Apres Mikhael Gromov, by Ghys, da la Harpe
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- Qa faut avouer, dit Trouscaillon qui, dans cette simple ellipse, utilisait hyperboliquement Ie cercle vicieux de la parabole. - Bun, dit Ie Sanctimontronais, j'y vais. (R. Queneau, Zazie dans Ie metru, Chapitre X.) L'etude des groupes infinis a toujours ete en relation etroite avec des considerations geometriques: etude des deplacements de l'espace euclidien R3 (Jordan, 1868), programme d'Erlangen (Klein, 1872), travaux de Lie et Poincare. L'approche combinatoire des groupes, fondee sur la notion de presentation, remonte a Dyck (1882) mais doit son developpement en premier lieu a Dehn (des 1910) (voir [ChM]). Les resultats decisifs de Dehn sur les groupes fondamentaux des sur faces sont marques par un ingredient geometrique crucial qui est la couTbuTe negati.ve. C'est ce me-me ingredient qui est ala base du tra vail fondamental de Gromov sur les groupes hyperboliques, conune on Ie voit esquisse dans [Gr2, Gr4] et repris dans [Gr5]. Nous sonuues cOllvaincus que l'importance de ce travail dans Ie developpement. de la theorie des groupes est comparable it ceux deja cites de Klein et Dehll.
- Sales Rank: #1378731 in Books
- Published on: 1990-01-01
- Released on: 1990-01-01
- Original language: English
- Number of items: 1
- Dimensions: 7.99" h x .68" w x 5.00" l, .69 pounds
- Binding: Paperback
- 287 pages
Language Notes
Text: English, French
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