Topological structures of \(\omega\)-subsets in symplectic groups
type: Item
instance of: scholarly article
title: Topological structures of \(\omega\)-subsets in symplectic groups
zbMATH Open document ID: 0930.22001
DOI: 10.1007/BF02650669
publication date: 2000-02-07T00:00:00Z
review text: Specify a point \(\omega\) in the unit circle in the complex plane. The set of symplectic matrices, having this \(\omega\) as an eigenvalue, is a hypersurface in the real symplectic group. The paper is devoted to the study of topological structures of the above hypersurface and of its complement in the group. For example, it is shown that the surface has exactly two path-connected components and that those components are simply connected, etc.
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 37J10
zbMATH DE Number: 1321991
zbMATH Keywords: symplectic groups
zbMATH Keywords: \(\omega\)-subsets
zbMATH Keywords: topological structure
author: Yiming Long
reviewed by: Yuri E. Gliklikh
MaRDI profile type: Publication
cites work: New aspects in the theory of stability of Hamiltonian systems
cites work: Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
cites work: Morse theory for periodic solutions of hamiltonian systems and the maslov index
cites work: A Maslov-type index theory for symplectic paths
cites work: Normal forms of symplectic matrices
full work available at URL: https://doi.org/10.1007/bf02650669
OpenAlex ID: W2044593209
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1321991