Volume entropy semi-norm and systolic volume semi-norm
Ivan Babenko
Université de Montpellier, FranceStéphane Sabourau
Univ Paris Est Creteil, CNRS; Univ Gustave Eiffel, Marne-la-Vallée, France
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Abstract
We introduce the volume entropy semi-norm and the systolic volume semi-norm in real homology and show that they satisfy functorial properties similar to the ones of the simplicial volume. Along the way, we also establish a roughly optimal upper bound on the systolic volume of the multiples of any homology class. Finally, we prove that the volume entropy semi-norm, the systolic volume semi-norm and the simplicial volume semi-norm are equivalent in every dimension.
Cite this article
Ivan Babenko, Stéphane Sabourau, Volume entropy semi-norm and systolic volume semi-norm. J. Eur. Math. Soc. (2023), published online first
DOI 10.4171/JEMS/1370