Isoperimetric and isodiametric functions of groups

@article{Sapir1998IsoperimetricAI,
  title={Isoperimetric and isodiametric functions of groups},
  author={Mark V. Sapir and Jean-Camille Birget and Eliyahu Rips},
  journal={Annals of Mathematics},
  year={1998},
  volume={156},
  pages={345-466}
}
This is the first of two papers devoted to connections between asymptotic functions of groups and computational complexity. In particular, we show how to construct a finitely presented group with NP-complete word problem. One of the main results of this paper states that if a real number cx > 4 is computable in time 0 then na is equivalent ( "big O" ) to the Dehn function of a finitely presented group. The smallest isodiametric function of this group is n3°8/4. On the other hand, if na is… 
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