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A condition that prevents groups from acting fixed point free on cube complexes

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Abstract

We describe a group theoretic condition which ensures that any strongly simplicial action of a group satisfying this condition on a CAT\((0)\) cube complex has a global fixed point. In particular, we show that this fixed point criterion is satisfied by Aut\((F_n)\), the automorphism group of a free group of rank n. For SAut\((F_n)\), the unique subgroup of index two in Aut\((F_n)\), we obtain a similar result.

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Acknowledgements

The author would like to thank Yves Cornulier and Genevois Anthony for their comments concerning completeness in Proposition 2.2 and the referee for many helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Münster University, Einsteinstrasse 62, 48149, Münster, Germany

    Olga Varghese

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  1. Olga Varghese
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Correspondence to Olga Varghese.

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Research partially supported by SFB 878.

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Varghese, O. A condition that prevents groups from acting fixed point free on cube complexes. Geom Dedicata 200, 85–91 (2019). https://doi.org/10.1007/s10711-018-0361-2

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  • DOI: https://doi.org/10.1007/s10711-018-0361-2

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