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

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

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

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1007/s00022-023-00685-3

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title = "Extending Gromov{\textquoteright}s optimal systolic inequality",

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{\textquoteright}s inequality to manifolds whose fundamental cohomology class is a cup product of 2-dimensional classes.",

author = "Goodwillie, {Thomas G.} and Hebda, {James J.} and Katz, {Mikhail G.}",

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year = "2023",

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doi = "10.1007/s00022-023-00685-3",

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AU - Hebda, James J.

AU - Katz, Mikhail G.

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AB - 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.

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DO - 10.1007/s00022-023-00685-3

M3 - مقالة

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VL - 114

JO - Journal of Geometry

JF - Journal of Geometry

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M1 - 23

ER -

Extending Gromov’s optimal systolic inequality

Abstract

All Science Journal Classification (ASJC) codes

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