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Holomorphic approximation for Hamiltonian diffeomorphism groups via the Symplectic Density Property
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.
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BibTeX
@misc{huang2026holomorphic,
title = {{Holomorphic approximation for Hamiltonian diffeomorphism groups via the Symplectic Density Property}},
author = {Gaofeng Huang and Frank Kutzschebauch},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13718},
eprint = {2610.13718},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13718},
}
RIS
TY - UNPB
TI - Holomorphic approximation for Hamiltonian diffeomorphism groups via the Symplectic Density Property
AU - Gaofeng Huang
AU - Frank Kutzschebauch
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13718
UR - https://arxiv.org/abs/2610.13718
AB - 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.
ER -