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

Brown University
Saint Louis University

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

3 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

Access to Document

10.1007/s00022-023-00685-3

Cite this

@article{064fc748150247808d59283795c84cd3,

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.\}",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2023",

month = aug,

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

language = "אנגלית",

volume = "114",

journal = "Journal of Geometry",

issn = "0047-2468",

publisher = "Springer International Publishing",

number = "2",

}

TY - JOUR

T1 - Extending Gromov’s optimal systolic inequality

AU - Goodwillie, Thomas G.

AU - Hebda, James J.

AU - Katz, Mikhail G.

PY - 2023/8

Y1 - 2023/8

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/85167444094

U2 - 10.1007/s00022-023-00685-3

DO - 10.1007/s00022-023-00685-3

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85167444094

SN - 0047-2468

VL - 114

JO - Journal of Geometry

JF - Journal of Geometry

IS - 2

M1 - 23

ER -

Extending Gromov’s optimal systolic inequality

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this