2008, 2(3): 499-507. doi: 10.3934/jmd.2008.2.499

Irrational stable commutator length in finitely presented groups

1. 

Department of Mathematics, Caltech, Pasadena, CA 91125, United States

Received  January 2008 Published  April 2008

We give examples of finitely presented groups containing elements with irrational (in fact, transcendental) stable commutator length, thus answering in the negative a question of M. Gromov. Our examples come from 1-dimensional dynamics and are related to the generalized Thompson groups studied by M. Stein, I. Liousse and others.
Citation: Dongping Zhuang. Irrational stable commutator length in finitely presented groups. Journal of Modern Dynamics, 2008, 2 (3) : 499-507. doi: 10.3934/jmd.2008.2.499
[1]

Ferrán Valdez. Veech groups, irrational billiards and stable abelian differentials. Discrete & Continuous Dynamical Systems - A, 2012, 32 (3) : 1055-1063. doi: 10.3934/dcds.2012.32.1055

[2]

Zhifeng Dai, Fenghua Wen. A generalized approach to sparse and stable portfolio optimization problem. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-16. doi: 10.3934/jimo.2018025

[3]

Roman Shvydkoy, Eitan Tadmor. Eulerian dynamics with a commutator forcing II: Flocking. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5503-5520. doi: 10.3934/dcds.2017239

[4]

Viorel Niţică. Stable transitivity for extensions of hyperbolic systems by semidirect products of compact and nilpotent Lie groups. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 1197-1204. doi: 10.3934/dcds.2011.29.1197

[5]

J. M. Peña. Refinable functions with general dilation and a stable test for generalized Routh-Hurwitz conditions. Communications on Pure & Applied Analysis, 2007, 6 (3) : 809-818. doi: 10.3934/cpaa.2007.6.809

[6]

Dmitry Dolgopyat, Dmitry Jakobson. On small gaps in the length spectrum. Journal of Modern Dynamics, 2016, 10: 339-352. doi: 10.3934/jmd.2016.10.339

[7]

Arthur Henrique Caixeta, Irena Lasiecka, Valéria Neves Domingos Cavalcanti. On long time behavior of Moore-Gibson-Thompson equation with molecular relaxation. Evolution Equations & Control Theory, 2016, 5 (4) : 661-676. doi: 10.3934/eect.2016024

[8]

Luciano Abadías, Carlos Lizama, Marina Murillo-Arcila. Hölder regularity for the Moore-Gibson-Thompson equation with infinite delay. Communications on Pure & Applied Analysis, 2018, 17 (1) : 243-265. doi: 10.3934/cpaa.2018015

[9]

Feng Luo. Geodesic length functions and Teichmuller spaces. Electronic Research Announcements, 1996, 2: 34-41.

[10]

Michael Khanevsky. Hofer's length spectrum of symplectic surfaces. Journal of Modern Dynamics, 2015, 9: 219-235. doi: 10.3934/jmd.2015.9.219

[11]

Masaaki Harada, Akihiro Munemasa. Classification of self-dual codes of length 36. Advances in Mathematics of Communications, 2012, 6 (2) : 229-235. doi: 10.3934/amc.2012.6.229

[12]

Boris P. Belinskiy. Optimal design of an optical length of a rod with the given mass. Conference Publications, 2007, 2007 (Special) : 85-91. doi: 10.3934/proc.2007.2007.85

[13]

Kenneth R. Meyer, Jesús F. Palacián, Patricia Yanguas. Normally stable hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2013, 33 (3) : 1201-1214. doi: 10.3934/dcds.2013.33.1201

[14]

Rasul Shafikov, Christian Wolf. Stable sets, hyperbolicity and dimension. Discrete & Continuous Dynamical Systems - A, 2005, 12 (3) : 403-412. doi: 10.3934/dcds.2005.12.403

[15]

Xiao Wen. Structurally stable homoclinic classes. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1693-1707. doi: 10.3934/dcds.2016.36.1693

[16]

Alex Potapov, Ulrike E. Schlägel, Mark A. Lewis. Evolutionarily stable diffusive dispersal. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3319-3340. doi: 10.3934/dcdsb.2014.19.3319

[17]

Neal Koblitz, Alfred Menezes. Another look at generic groups. Advances in Mathematics of Communications, 2007, 1 (1) : 13-28. doi: 10.3934/amc.2007.1.13

[18]

Sergei V. Ivanov. On aspherical presentations of groups. Electronic Research Announcements, 1998, 4: 109-114.

[19]

Emmanuel Breuillard, Ben Green, Terence Tao. Linear approximate groups. Electronic Research Announcements, 2010, 17: 57-67. doi: 10.3934/era.2010.17.57

[20]

Benjamin Weiss. Entropy and actions of sofic groups. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3375-3383. doi: 10.3934/dcdsb.2015.20.3375

2016 Impact Factor: 0.706

Metrics

  • PDF downloads (1)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]