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Introduction to a small cancellation theorem
Stéphane Lamy1; Anne Lonjou2
1 Institut de Mathématiques de Toulouse UMR 5219, Université de Toulouse, UPS F-31062 Toulouse Cedex 9, France
2 Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, 4051 Basel, Switzerland
Confluentes Mathematici, Volume 13 (2021) no. 1, pp. 79-102.

This note is intended as an introduction to two previous works respectively by Dahmani, Guirardel, Osin, and by Cantat, Lamy. We give two proofs of a Small Cancellation Theorem for groups acting on a simplicial tree. We discuss the application to the group of plane polynomial automorphisms over any ground field.

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DOI: 10.5802/cml.73
Classification: 20F06, 20E08, 14R10
Keywords: Small cancellation, group action on tree, polynomial automorphisms

Stéphane Lamy 1; Anne Lonjou 2

1 Institut de Mathématiques de Toulouse UMR 5219, Université de Toulouse, UPS F-31062 Toulouse Cedex 9, France
2 Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, 4051 Basel, Switzerland
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Stéphane Lamy; Anne Lonjou. Introduction to a small cancellation theorem. Confluentes Mathematici, Volume 13 (2021) no. 1, pp. 79-102. doi : 10.5802/cml.73. https://cml.centre-mersenne.org/articles/10.5802/cml.73/

[1] M. Bestvina and K. Fujiwara. Bounded cohomology of subgroups of mapping class groups. Geometry and Topology, 6:69–89 (electronic), 2002. | DOI | MR | Zbl

[2] C. Champetier. Petite simplification dans les groupes hyperboliques. Ann. Fac. Sci. Toulouse Math. (6), 3(2):161–221, 1994. | DOI | MR | Zbl

[3] S. Cantat and S. Lamy. Normal subgroups in the Cremona group. Acta Math., 210(1):31–94, 2013. With an appendix by Yves de Cornulier. | DOI | MR | Zbl

[4] V. I. Danilov. Non-simplicity of the group of unimodular automorphisms of an affine plane. Mat. Zametki, 15:289–293, 1974. | DOI

[5] T. Delzant. Sous-groupes distingués et quotients des groupes hyperboliques. Duke Math. J., 83(3):661–682, 1996. | DOI | Zbl

[6] F. Dahmani, V. Guirardel and D. Osin. Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces. Mem. Amer. Math. Soc., 245(1156), 2017. | DOI | MR | Zbl

[7] P. de la Harpe. Topics in geometric group theory. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 2000. | Zbl

[8] J.-P. Furter and S. Lamy. Normal subgroup generated by a plane polynomial automorphism. Transform. Groups, 15(3):577–610, 2010. | DOI | MR | Zbl

[9] M. Gromov. Hyperbolic groups. In Essays in group theory, volume 8 of Math. Sci. Res. Inst. Publ., pages 75–263. Springer, New York, 1987. | DOI | Zbl

[10] S. Lamy. L’alternative de Tits pour Aut [ℂ 2 ]. J. Algebra, 239(2):413–437, 2001. | DOI | Zbl

[11] S. Lamy. Une preuve géométrique du théorème de Jung. Enseign. Math. (2), 48(3-4):291–315, 2002. | Zbl

[12] A. Lonjou. Non simplicité du groupe de Cremona sur tout corps. Ann. Inst. Fourier (Grenoble), 66(5):2021–2046, 2016. | DOI | Zbl

[13] R. C. Lyndon and P. E. Schupp. Combinatorial group theory. Springer-Verlag, Berlin-New York, 1977. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89.

[14] A. Minasyan and D. Osin. Acylindrical hyperbolicity of groups acting on trees. Math. Ann., 362(3–4):1055–1105, 2015. | DOI | MR | Zbl

[15] A. Y. Ol’shanskiĭ. SQ -universality of hyperbolic groups. Mat. Sb., 186(8):119–132, 1995. | MR

[16] J.-P. Serre. Trees. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2003. Translated from the French original by John Stillwell, Corrected 2nd printing of the 1980 English translation.

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