Extending Gromov’s optimal systolic inequality

Thomas G. Goodwillie, James J. Hebda, Mikhail G. Katz

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The existence of nontrivial cup products or Massey products in the cohomology of a manifold leads to inequalities of systolic type, but in general such inequalities are not optimal (tight). Gromov proved an optimal systolic inequality for complex projective space. We provide a natural extension of Gromov’s inequality to manifolds whose fundamental cohomology class is a cup product of 2-dimensional classes.

Original languageEnglish
Article number23
JournalJournal of Geometry
Issue number2
StatePublished - Aug 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.


Mikhail Katz is partially supported by the BSF Grant 2020124 and the ISF Grant 743/22.

FundersFunder number
United States-Israel Binational Science Foundation2020124
Israel Science Foundation743/22


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