Work

Holomorphic approximation for Hamiltonian diffeomorphism groups via the Symplectic Density Property

Year: 2026

Type: preprint

Abstract: We show that the cotangent bundle of a holomorphically flexible Stein manifold has the symplectic density property. As application we deduce holomorphic approximation for Hamiltonian diffeomorphisms of real cotangent bundles by complex symplectic automorphisms of the complexified cotangent bundles, which preserve the real bundle, in the Carleman sense, i.e. in the Whitney topology.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.13718

Authors: Huang, Gaofeng, Kutzschebauch, Frank

Institutions: University of Bern, Harvard University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Awards: Symplectic Density Property and Approximation of Real Symmetry by Complex Symmetry, Equivariant Oka Principle and symplectic density property

OpenAlex ID: W7221564046

Cites: 24

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Related to: 10