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Identifying Dehn functions of Bestvina–Brady groups from their defining graphs

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Abstract

Let \(\Gamma \) be a finite simplicial graph such that the flag complex on \(\Gamma \) is a 2-dimensional triangulated disk. We show that with some assumptions, the Dehn function of the associated Bestvina–Brady group is either quadratic, cubic, or quartic. Furthermore, we can identify the Dehn function from the defining graph \(\Gamma \).

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Acknowledgements

I want to thank Pallavi Dani for introducing me to this project and her generous advice. I want to thank Tullia Dymarz, Max Forester, and Bogdan Oporowski for many helpful conversations and their support. I want to thank the referee for valuable suggestions and feedback.

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  1. Oxford College of Emory University, 801 Emory Street, Oxford, GA, 30054, USA

    Yu-Chan Chang

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Correspondence to Yu-Chan Chang.

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The author gratefully acknowledges the support from the NSF Grant DMS-1812061.

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Chang, YC. Identifying Dehn functions of Bestvina–Brady groups from their defining graphs. Geom Dedicata 214, 211–239 (2021). https://doi.org/10.1007/s10711-021-00612-3

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  • DOI: https://doi.org/10.1007/s10711-021-00612-3

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