Huang, Gaofeng (2025). Density Property of Stein Manifolds and Holomorphic Matrix Factorization. (Thesis). Universität Bern, Bern
|
Text
25huang_g.pdf - Thesis Available under License Creative Commons: Attribution (CC-BY 4.0). Download (878kB) | Preview |
Abstract
We present results on the density property of Stein manifolds and on factorization of holomorphic matrices. A Stein manifold with the density property has an infinite dimensional group of holomorphic automorphisms. We generalize a criterion for the density property. As an application, we find new examples of Stein manifolds with the density property. We also work with the symplectic density property and the Hamiltonian density property. We establish these properties for the Calogero–Moser space of n particles and describe its group of holomorphic symplectic automorphisms. This gives a new class of Stein manifolds with the symplectic density property besides even dimensional Euclidean spaces. The real Calogero–Moser space CRn is a noncompact, totally real submanifold of the complex Calogero–Moser space Cn. We prove that every symplectic diffeomorphism of CRn smoothly isotopic to the identity can be approximated in the fine Whitney topology – the strongest in this context – by holomorphic symplectic automorphisms of Cn that preserve CRn. A key ingredient in our proof is a refined version of the symplectic density property of Cn. In holomorphic matrix factorization we factor a matrix, which has holomorphic functions on a Stein space as entries, into a product of specific matrices, e.g. unitriangular matrices or exponentials. In the final part we analyze bounds for the number of factors in some holomorphic matrix factorizations.
| Item Type: | Thesis |
|---|---|
| Dissertation Type: | Single |
| Date of Defense: | 27 June 2025 |
| Subjects: | 500 Science > 510 Mathematics |
| Institute / Center: | 08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
| Depositing User: | Hammer Igor |
| Date Deposited: | 15 Jul 2025 16:20 |
| Last Modified: | 15 Jul 2025 16:20 |
| URI: | https://boristheses.unibe.ch/id/eprint/6381 |
Actions (login required)
 |
View Item |