Extending Gromov's optimal systolic inequality
Differential Geometry
2024-07-08 v1
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.
Cite
@article{arxiv.2407.03803,
title = {Extending Gromov's optimal systolic inequality},
author = {Thomas G. Goodwillie and James J. Hebda and Mikhail G. Katz},
journal= {arXiv preprint arXiv:2407.03803},
year = {2024}
}
Comments
8 pages, published in Journal of Geometry