Work

On the intersection form of fillings

Year: 2024

Type: article

Abstract: We prove, by an ad hoc method, that exact fillings with vanishing rational first Chern class of flexibly fillable contact manifolds have unique integral intersection forms. We appeal to the special Reeb dynamics (stronger than ADC in [Lazarev, Geom. Funct. Anal. 30 (2020), no. 1, 188–254]) on the contact boundary, while a more systematic approach working for general ADC manifolds is developed independently by Eliashberg, Ganatra and Lazarev. We also discuss cases where the vanishing rational first Chern class assumption can be removed. We derive the uniqueness of diffeomorphism types of exact fillings of certain flexibly fillable contact manifolds and obstructions to contact embeddings, which are not necessarily exact.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.12981

Author: Zhengyi Zhou

Institutions: Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China

Awards: G4712210066, G8236475572, G8533620077