American Institute of Mathematical Sciences

July  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
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