Homological and homotopical Dehn functions are different

@article{Abrams2013HomologicalAH,
  title={Homological and homotopical Dehn functions are different},
  author={Aaron Abrams and Noel Brady and Pallavi Dani and Robert Young},
  journal={Proceedings of the National Academy of Sciences},
  year={2013},
  volume={110},
  pages={19206 - 19212}
}
The homological and homotopical Dehn functions are different ways of measuring the difficulty of filling a closed curve inside a group or a space. The homological Dehn function measures fillings of cycles by chains, whereas the homotopical Dehn function measures fillings of curves by disks. Because the two definitions involve different sorts of boundaries and fillings, there is no a priori relationship between the two functions; however, before this work, there were no known examples of… 

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