Work

Symplectic topology and ideal-valued measures

Year: 2024

Type: article

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 allows 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 Varolgüneş.

Source: Selecta Mathematica

DOI: 10.1007/s00029-024-00967-x

Authors: Adi Dickstein, Yaniv Ganor, Leonid Polterovich, Frol Zapolsky

Institutions: Tel Aviv University, Holon Institute of Technology, Serbian Academy of Sciences and Arts, University of Haifa

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Milner Foundation, University of Haifa