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

Irrational stable commutator length in finitely presented groups

Dongping Zhuang 1,

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.
Keywords: Stable commutator length, generalized Thompson groups..
Mathematics Subject Classification: Primary: 20F12, 37E45; Secondary: 37E1.
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
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