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13 - Boundaries of Zn-Free Groups

Published online by Cambridge University Press:  20 July 2017

Andrei Malyutin
Affiliation:
St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russia
Tatiana Nagnibeda
Affiliation:
Section de Mathématiques, University of Geneva, 2-4 Rue du Lièvre, Case Postale 64, 1211 Genève 4, Suisse
Denis Serbin
Affiliation:
Department of Mathematical Sciences, Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07030, USA
Tullio Ceccherini-Silberstein
Affiliation:
Università degli Studi del Sannio, Italy
Maura Salvatori
Affiliation:
Università degli Studi di Milano
Ecaterina Sava-Huss
Affiliation:
Cornell University, New York
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Print publication year: 2017

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References

[1] R., Alperin and H., Bass. Length functions of group actions on trees. In Combinatorial group theory and topology, ed. S. M. Gersten and J. R. Stallings, vol. 111 of Annals of Math. Studies, pp. 265–378. Princeton University Press, 1987.
[2] H., Bass. Group actions on non-Archimedean trees. In Arboreal group theory, vol. 19 of MSRI Publications, pp. 69–131, New York: Springer- Verlag, 1991.
[3] M., Bestvina and M., Feighn Stable actions of groups on real trees. Invent. Math., 2(2):287–321, 1995.Google Scholar
[4] I., Bumagin and O., Kharlampovich. Z n-free groups are CAT(0). J. London Math. Soc., 3(3):761–78, 2013.Google Scholar
[5] D. I., Cartwright and P. M., Soardi. Convergence to ends for random walks on the automorphism group of a tree. Proc. Amer. Math. Soc., 107:817–23, 1989.Google Scholar
[6] I., Chiswell. Abstract length functions in groups. Math. Proc. Cambridge Philos. Soc., 3(3):451–63, 1976.Google Scholar
[7] I., Chiswell. Introduction to trees. Singapore: World Scientific, 2001.
[8] D. E., Cohen. Combinatorial group theory: a topological approach, vol. 14 of London Mathematical Society Student Texts. Cambridge University Press, 1989.
[9] F., Dahmani. Combination of convergence groups. Geom. Topol., 7:933–63, 2003.Google Scholar
[10] H., Furstenberg. Boundary theory and stochastic processes on homogeneous spaces. In Harmonic analysis on homogeneous spaces, vol. 26 of Proc. Sympos. Pure Math., pp. 193–229, Providence, RI: American Mathematical Society, 1973.
[11] D., Gaboriau, G., Levitt, and F., Paulin. Pseudogroups of isometries of R and Rips' Theorem on free actions on R-trees. Israel. J. Math., 87:403–28, 1994.Google Scholar
[12] V., Gerasimov. Floyd maps for relatively hyperbolic groups. GAFA, 5(5):1361–99, 2012.Google Scholar
[13] V., Gerasimov and L., Potyagailo. Quasi-isometric maps and Floyd boundaries of relatively hyperbolic groups. J. Eur. Math. Soc., 6(6):2115–37, 2013.Google Scholar
[14] V., Guirardel. Limit groups and groups acting freely on R n-trees. Geom. Topol., 8:1427–70, 2004.Google Scholar
[15] V. A., Kaimanovich. The Poisson formula for groups with hyperbolic properties. Ann. of Math., 152:659–92, 2000.Google Scholar
[16] V. A., Kaimanovich and H., Masur. The Poisson boundary of the mapping class group. Invent. Math., 2(2):221–64, 1996.Google Scholar
[17] A., Karlsson. Free subgroups of groups with non-trivial Floyd boundary. Comm. Algebra, 31:5361–76, 2003.Google Scholar
[18] A., Karlsson and G., Margulis. A Multiplicative Ergodic Theorem and Nonpositively Curved Spaces. Commun. Math. Phys., 208:107–23, 1999.Google Scholar
[19] O., Kharlampovich, A. G., Myasnikov, V. N., Remeslennikov, and D., Serbin. Groups with free regular length functions in Zn. Trans. Amer. Math. Soc., 364:2847–82, 2012.Google Scholar
[20] O., Kharlampovich, A. G., Myasnikov, and D., Serbin. Actions, length functions, and non-archemedian words. Internat. J. Algebra Comput., 2(2):325–455, 2013.Google Scholar
[21] O., Kharlampovich, A. G., Myasnikov, and D., Serbin. Infinite words and universal free actions. Groups, Complexity, Cryptology, 1(1):55–69, 2014.Google Scholar
[22] O., Kharlampovich, A. G., Myasnikov, and D., Serbin. Regular completions of Zn-free groups. Sumbitted, Available at http://arxiv.org/abs/1208.4640, 2016.
[23] R., Lyndon. Length functions in groups. Math. Scand., 12:209–34, 1963.Google Scholar
[24] A. V., Malyutin and A. M., Vershik. Boundaries of braid groups and the Markov–Ivanovsky normal form. Izv. RAN. Ser. Mat., 6(6):105–32, 2008.Google Scholar
[25] J., Morgan and P., Shalen. Valuations, trees, and degenerations of hyperbolic structures, I. Ann. of Math., 120:401–76, 1984.Google Scholar
[26] A., Nevo and M., Sageev. The Poisson boundary of CAT(0) cube complex groups. Groups, Geometry, and Dynamics, 3(3):653–95, 2013.Google Scholar
[27] J., Tits. A ‘theorem of Lie-Kolchin’ for trees. In Contributions to algebra: a collection of papers dedicated to Ellis Kolchin, pp. 377–88. New York: Academic Press: 1977.Google Scholar

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  • Boundaries of Zn-Free Groups
    • By Andrei Malyutin, St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russia, Tatiana Nagnibeda, Section de Mathématiques, University of Geneva, 2-4 Rue du Lièvre, Case Postale 64, 1211 Genève 4, Suisse, Denis Serbin, Department of Mathematical Sciences, Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07030, USA
  • Edited by Tullio Ceccherini-Silberstein, Università degli Studi del Sannio, Italy, Maura Salvatori, Università degli Studi di Milano, Ecaterina Sava-Huss, Cornell University, New York
  • Book: Groups, Graphs and Random Walks
  • Online publication: 20 July 2017
  • Chapter DOI: https://doi.org/10.1017/9781316576571.015
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  • Boundaries of Zn-Free Groups
    • By Andrei Malyutin, St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russia, Tatiana Nagnibeda, Section de Mathématiques, University of Geneva, 2-4 Rue du Lièvre, Case Postale 64, 1211 Genève 4, Suisse, Denis Serbin, Department of Mathematical Sciences, Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07030, USA
  • Edited by Tullio Ceccherini-Silberstein, Università degli Studi del Sannio, Italy, Maura Salvatori, Università degli Studi di Milano, Ecaterina Sava-Huss, Cornell University, New York
  • Book: Groups, Graphs and Random Walks
  • Online publication: 20 July 2017
  • Chapter DOI: https://doi.org/10.1017/9781316576571.015
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Boundaries of Zn-Free Groups
    • By Andrei Malyutin, St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russia, Tatiana Nagnibeda, Section de Mathématiques, University of Geneva, 2-4 Rue du Lièvre, Case Postale 64, 1211 Genève 4, Suisse, Denis Serbin, Department of Mathematical Sciences, Stevens Institute of Technology, 1 Castle Point on Hudson, Hoboken, NJ 07030, USA
  • Edited by Tullio Ceccherini-Silberstein, Università degli Studi del Sannio, Italy, Maura Salvatori, Università degli Studi di Milano, Ecaterina Sava-Huss, Cornell University, New York
  • Book: Groups, Graphs and Random Walks
  • Online publication: 20 July 2017
  • Chapter DOI: https://doi.org/10.1017/9781316576571.015
Available formats
×