Skip Navigation

Journal of Topology 2008 1(4):804-836; doi:10.1112/jtopol/jtn023
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Delzant, T.
Right arrow Articles by Gromov, M.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008 London Mathematical Society

Courbure mésoscopique et théorie de la toute petite simplification

Thomas Delzant

IRMA, Université de Strasbourg, 7 rue R. Descartes, 67084 Strasbourg, France delzant@math.u-strasbourg

Misha Gromov

IHES, 35, route de Chartres, 91440 Bures-sur-Yvette, France gromov@ihes.fr

We present an asymptotic approach to small cancellation theory, and apply this method to the study of the Burnside groups.

Received May 8, 2007.

2000 Mathematics Subject Classification AMS classification 20F05, 20F65, 20F67



References

  1. Adian S. I. The Burnside problem and identities in groups (1979) Berlin and New York: Springer. Ergebnisse der Math. 95.
  2. Adian S. I., Lysionok I. G. The method of classification of periodic words and the Burnside problem. In: Proceedings of the International Conference on Algebra, Part 1 (1992) Providence, RI: American Mathematical Society. 13–28. Contemporary Mathematics 131.
  3. Bridson M. R., Haefliger A. Metric spaces of non-positive curvature (1999) Berlin: Springer. Grund. Math. Wiss. 319.
  4. Benedetti R., Petronio C. Lectures on hyperbolic geometry (1992) Berlin: Springer. Universitext.
  5. Bowditch B. H. Notes on Gromov’s hyperbolicity criterion for path-metric spaces. In: Group theory from a geometrical viewpoint—Ghys E., Haefliger A., Verjovsky A., eds. (1991) River Edge, NJ: World Scientific. 64–167. Trieste, 1990.
  6. Champetier C. Petite simplification dans les groupes hyperboliques. Ann. fac. sci. Toulouse (1994) 3:161–221.
  7. Coornaert M., Delzant T., Papadopoulos A. Les groupes hyperboliques de Gromov (1990) Berlin: Springer. Lecture Notes in Mathematics 1441.
  8. Delzant T. Sous-groupes distingués et quotients des groupes hyperboliques. Duke Math. J. (1996) 83(3):661–682.[CrossRef]
  9. Drutu C. Quasi-isometry invariants and asymptotic cones. Int. J. Algebra Comput. (2002) 12(1-2):99–135.[CrossRef]
  10. Euclide. Les oeuvres d'Euclide (1966) Paris: Albert Blanchard.
  11. Ghys E., de la Harpe P. Sur les groupes hyperboliques. In: d'après Mikhael Gromov, Bern, 1988 (1990) Boston, MA: Birkhäuser. Progress in Mathematics 83.
  12. Greendlinger M. Dehn’s algorithm for the word problem. Commun. Pure Appl. Math (1960) 13:67–83.[CrossRef]
  13. Grigorchuk R. I., Lysenok I. G. The Burnside problems. In: The concise handbook of algebra—Alexander V. Mikhalev, Günter F. Pilz, eds. (2002) Dordrecht: Kluwer.
  14. Gromov M. Hyperbolic groups. In: Essays in group theory—Gersten S., ed. (1987) New York: Springer. MSRI 8.
  15. Gromov M. Mesoscopic curvature and hyperbolicity. In: Global differential geometry: the mathematical legacy of Alfred Gray (2001) Providence, RI: American Mathematical Society. 58–69. Contemporary Mathematics 288.
  16. Gromov M. Metric structures for Riemannian and non-Riemannian spaces (1999) Boston, MA: Birkhäuser. Progress in Mathematics 152.
  17. Haefliger A. Complex of groups and orbihedra. In: Group theory from a geometrical viewpoint—Ghys E., Haefliger A., Verjovsky A., eds. (1991) River Edge, NJ: World Scientific. 504–540. Trieste, 1990.
  18. Ivanov S. V. The free Burnside groups of sufficiently large exponent. Int. J. Algebra Comput (1994) 4:1–307.[CrossRef]
  19. Ivanov S. V., Olshanskii A. Yu. Hyperbolic groups and their quotients of bounded exponents. Trans. Amer. Math. Soc. (1996) 348(6):2091–2138.[CrossRef]
  20. Lyndon R. C. On Dehn’s algorithm. Math. Ann. (1966) 166:208–228.[CrossRef]
  21. Lyndon R. C., Schupp P. E. Combinatorial group theory. In: Ergebnisse der Mathematik und ihrer Grenzgebiete (1977) 89. Berlin and New York: Springer.
  22. Lysenok I. G. Infinite Burnside groups of even exponent. Izv. Math. (1996) 60(3):453–654.[CrossRef]
  23. Olshanskii A. Yu. The Novikov–Adian theorem. Mat. Sb. (N.S.). 118(160) (1982) no. 2, 203–235, 287.
  24. Olshanskii A. Yu. Geometry of defining relations in groups (1991) Dordrecht: Kluwer. Mathematics and its Applications (Soviet Series) 70.
  25. Rips E. Generalized small cancellation theory and its application I: The word problem. Israel J. Math. (1982) 41(2):1–146.[CrossRef]
  26. Serre J.-P. Arbres, amalgames, SL2. Astérisque (1977) 46.
  27. Tartakovskii V. A. Solution of the word problem for groups with a k-reduced basis for k > 6'. Izv. Akad. Nauk. SSSR. Ser. Mat. (1949) 13:483–494. (Russian).

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Delzant, T.
Right arrow Articles by Gromov, M.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?