Topological and Homological Properties of the Orbit Space of a Compact Linear Lie Group with a Commutative Connected Component
Authors: Styrt O.G. | Published: 08.06.2018 |
Published in issue: #3(78)/2018 | |
DOI: 10.18698/1812-3368-2018-3-68-81 | |
Category: Mathematics and Mechanics | Chapter: Substantial Analysis, Complex and Functional Analysis | |
Keywords: Lie group, linear representation of a group, topological quotient of an action, topological manifold, homological manifold, linear representation of a group, topological quotient of an action |
The purpose of the work was to find whether the compact linear group space factor is a topological manifold, as well as a homological manifold. The paper studied the case of an infinite group with a commutative connected component. In previous research a method of reducing an arbitrary representation to a representation with a 2-stable set of weights was introduced. Findings of the research helped to obtain important necessary conditions in the case of a 2-stable weight set
This work was supported by a grant from the RFBR (no. 16-01-00818-a)
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