Symplectic topology and ideal-valued measures
Symplectic Geometry
2024-03-26 v3 Algebraic Topology
Abstract
We adapt Gromov's notion of ideal-valued measures to symplectic topology, and use it for proving new results on symplectic rigidity and symplectic intersections. Furthermore, it enables us to discuss three "big fiber theorems", the Centerpoint Theorem in combinatorial geometry, the Maximal Fiber Inequality in topology, and the Non-displaceable Fiber Theorem in symplectic topology, from a unified viewpoint. Our main technical tool is an enhancement of the symplectic cohomology theory recently developed by Varolgunes.
Keywords
Cite
@article{arxiv.2107.10012,
title = {Symplectic topology and ideal-valued measures},
author = {Adi Dickstein and Yaniv Ganor and Leonid Polterovich and Frol Zapolsky},
journal= {arXiv preprint arXiv:2107.10012},
year = {2024}
}
Comments
99 pages, 4 figures, small corrections, exposition revised