More on the Topological and Homological Properties of the Orbit Space in a Compact Linear Lie Group Featuring a Commutative Connected Component. Conclusion
| Authors: Styrt O.G. | Published: 05.12.2018 |
| Published in issue: #6(81)/2018 | |
| DOI: 10.18698/1812-3368-2018-6-48-63 | |
| Category: Mathematics and Mechanics | Chapter: Substantial Analysis, Complex and Functional Analysis | |
| Keywords: Lie group, linear representation, topological quotient of an action, topological manifold, homology manifold | |
The investigation concerns the problem of whether the quotient space of a compact linear group is a topological and homology manifold. We consider the case of an infinite group featuring a commutative connected component. We present a technique for reducing an arbitrary representation to a representation featuring an indecomposable 2-stable set of weights that contains no zeros. We derived explicit criteria for a one-dimensional group and a higher dimensional group separately
The study was supported by the RFBR (grant no. 16-01-00818-a)
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