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Irrational stable commutator length in finitely presented groups

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  • 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.
    Mathematics Subject Classification: Primary: 20F12, 37E45; Secondary: 37E10.

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