Bestvina--Brady groups are subgroups of right-angled Artin groups, and their Dehn functions are bounded above by quartic functions. There are examples of Bestvina--Brady groups whose Dehn functions are linear, quadratic, cubic, and quartic. In this talk, I will give a class of Bestvina--Brady groups that have polynomial Dehn functions, and we can identify the Dehn functions by the defining graphs of those Bestvina--Brady groups.
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