Abstract
It is shown that a finitely generated branch group has Serre’s property (FA) if and only if it does not surject onto the infinite cyclic group or the infinite dihedral group. An example of a finitely generated self-similar branch group surjecting onto the infinite cyclic group is constructed.
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Partially supported by NSF grants DMS-0600975 and DMS-0456185.
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Dedicated to the memory of Sasha Reznikov
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Delzant, T., Grigorchuk, R. (2007). Homomorphic Images of Branch Groups, and Serre’s Property (FA). In: Kapranov, M., Manin, Y.I., Moree, P., Kolyada, S., Potyagailo, L. (eds) Geometry and Dynamics of Groups and Spaces. Progress in Mathematics, vol 265. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8608-5_7
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