Geodesic
Topological and homological properties of the orbit space of a~simple three-dimensional compact linear Lie group
Čebyševskij sbornik, Tome 23 (2022) no. 3, pp. 169-177.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article is devoted to the question whether the orbit space of a compact linear group is a topological manifold and a homological manifold. In the paper, the case of a simple three-dimensional group is considered. An upper bound is obtained for the sum of the half-dimension integral parts of the irreducible components of a representation whose quotient space is a homological manifold, that enhances an earlier result giving the same bound if the quotient space of a representation is a smooth manifold. The most of the representations satisfying this bound are also researched before. In the proofs, standard arguments from linear algebra, theory of Lie groups and algebras and their representations are used.
Keywords: Lie group, linear representation of a group, topological quotient space of an action, topological manifold, homological manifold. 
@article{CHEB_2022_23_3_a11,
     author = {O. G. Styrt},
     title = {Topological and homological properties of the orbit space of a~simple three-dimensional compact linear {Lie} group},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {169--177},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2022_23_3_a11/}
}
TY  - JOUR
AU  - O. G. Styrt
TI  - Topological and homological properties of the orbit space of a~simple three-dimensional compact linear Lie group
JO  - Čebyševskij sbornik
PY  - 2022
SP  - 169
EP  - 177
VL  - 23
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2022_23_3_a11/
LA  - ru
ID  - CHEB_2022_23_3_a11
ER  - 
%0 Journal Article
%A O. G. Styrt
%T Topological and homological properties of the orbit space of a~simple three-dimensional compact linear Lie group
%J Čebyševskij sbornik
%D 2022
%P 169-177
%V 23
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2022_23_3_a11/
%G ru
%F CHEB_2022_23_3_a11
O. G. Styrt. Topological and homological properties of the orbit space of a~simple three-dimensional compact linear Lie group. Čebyševskij sbornik, Tome 23 (2022) no. 3, pp. 169-177. http://geodesic.mathdoc.fr/item/CHEB_2022_23_3_a11/

[1] Mikhailova M. A., “O faktorprostranstve po deistviyu konechnoi gruppy, porozhdennoi psevdootrazheniyami”, Izv. AN SSSR. Ser. matem., 1984, no. 1(48), 104–126 | DOI | Zbl

[2] Lange C., When is the underlying space of an orbifold a topological manifold?, arXiv: math.GN/1307.4875

[3] Styrt O. G., “O prostranstve orbit kompaktnoi lineinoi gruppy Li s kommutativnoi svyaznoi komponentoi”, Trudy MMO, 70, 2009, 235–287 | MR | Zbl

[4] Styrt O. G., “O prostranstve orbit trekhmernoi kompaktnoi lineinoi gruppy Li”, Izv. RAN. Ser. matem., 75:4 (2011), 165–188 | DOI | MR | Zbl

[5] Styrt O. G., “O prostranstve orbit neprivodimogo predstavleniya spetsialnoi unitarnoi gruppy”, Trudy MMO, 74, no. 1, 2013, 175–199 | Zbl

[6] Styrt O. G., “On the orbit spaces of irreducible representations of simple compact Lie groups of types $B$, $C$, and $D$”, J. Algebra, 415 (2014), 137–161 | DOI | MR | Zbl

[7] Styrt O. G., Topological and homological properties of the orbit space of a compact linear Lie group with commutative connected component, 2016, arXiv: math.AG/1607.06907 | MR

[8] Styrt O. G., “Topologicheskie i gomologicheskie svoistva prostranstva orbit kompaktnoi lineinoi gruppy Li s kommutativnoi svyaznoi komponentoi”, Vestnik MGTU im. N. E. Baumana. Ser. Est. nauki, 2018, no. 3, 68–81 | DOI

[9] Styrt O. G., “Topologicheskie i gomologicheskie svoistva prostranstva orbit kompaktnoi lineinoi gruppy Li s kommutativnoi svyaznoi komponentoi. Vyvody”, Vestnik MGTU im. N. E. Baumana. Ser. Est. nauki, 2018, no. 6, 48–63 | DOI

[10] Bredon G., Vvedenie v teoriyu kompaktnykh grupp preobrazovanii, Nauka, M., 1980, 440 pp.