Systolic geometry and simplicial complexity for groups

Ivan Babenko
  • Corresponding author
  • Institut Montpelliérain Alexander Grothendieck, Bat. 9, Université Montpellier 2, CC 051, Place Eugène Bataillon, 34095, Montpellier, Cedex 5, France
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, Florent Balacheff
  • Laboratoire Paul Painlevé, Bat. M2, Université de Lille – Sciences et Technologies, Cité Scientifique, 59655, Villeneuve d’Ascq, Cedex, France
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and Guillaume Bulteau
  • Institut Montpelliérain Alexander Grothendieck, Bat. 9, Université Montpellier 2, CC 051, Place Eugène Bataillon, 34095, Montpellier, Cedex 5, France
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Abstract

Twenty years ago Gromov asked about how large is the set of isomorphism classes of groups whose systolic area is bounded from above. This article introduces a new combinatorial invariant for finitely presentable groups called simplicial complexity that allows to obtain a quite satisfactory answer to his question. Using this new complexity, we also derive new results on systolic area for groups that specify its topological behaviour.

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