# Cone-equivalent nilpotent groups with different Dehn functions

@article{Isenrich2020ConeequivalentNG, title={Cone-equivalent nilpotent groups with different Dehn functions}, author={Claudio Llosa Isenrich and Gabriel Pallier and Romain Tessera}, journal={arXiv: Group Theory}, year={2020} }

For every $k\geqslant 3$, we exhibit a simply connected $k$-nilpotent Lie group $N_k$ whose Dehn function behaves like $n^k$, while the Dehn function of its associated Carnot graded group behaves like $n^{k+1}$. This property and its consequences allow us to reveal three new phenomena. First, since those groups have uniform lattices, this provides the first examples of pairs of finitely presented groups with bilipschitz asymptotic cones but with different Dehn functions. The second surprising…

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