Extending Gromov’s optimal systolic inequality

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

doi:10.1007/s00022-023-00685-3

Extending Gromov’s optimal systolic inequality

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

Department of Mathematics

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2 Scopus citations

Abstract

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 language	English
Article number	23
Journal	Journal of Geometry
Volume	114
Issue number	2
DOIs	https://doi.org/10.1007/s00022-023-00685-3
State	Published - Aug 2023

Bibliographical note

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

Funding

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

Funders	Funder number
United States-Israel Binational Science Foundation	2020124
Israel Science Foundation	743/22

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10.1007/s00022-023-00685-3

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Extending Gromov’s optimal systolic inequality

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