Journal of Modern Dynamics (JMD)

Irrational stable commutator length in finitely presented groups

Pages: 499 - 507, Issue 3, July 2008      doi:10.3934/jmd.2008.2.499

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Dongping Zhuang - Department of Mathematics, Caltech, Pasadena, CA 91125, United States (email)

Abstract: 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.

Keywords:  Stable commutator length, generalized Thompson groups.
Mathematics Subject Classification:  Primary: 20F12, 37E45; Secondary: 37E10.

Received: January 2008;      Available Online: April 2008.