Quantitative null-cobordism

@article{Chambers2018QuantitativeN,
  title={Quantitative null-cobordism},
  author={Gregory R. Chambers and Dominic Dotterrer and Fedor Manin and Shmuel Weinberger},
  journal={Journal of the American Mathematical Society},
  year={2018}
}
<p>For a given null-cobordant Riemannian <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-manifold, how does the minimal geometric complexity of a null-cobordism depend on the geometric complexity of the manifold? Gromov has conjectured that this dependence should be linear… 

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