Geodesic
Representation varieties of finite index subgroups of Baumslag–Solitar groups
Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 24-28 
V. V. Beniash-Kryvets; I. O. Govorushko. Representation varieties of finite index subgroups of Baumslag–Solitar groups. Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 24-28. http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a2/
@article{TIMB_2015_23_2_a2,
     author = {V. V. Beniash-Kryvets and I. O. Govorushko},
     title = {Representation varieties of finite index subgroups of {Baumslag{\textendash}Solitar} groups},
     journal = {Trudy Instituta matematiki},
     pages = {24--28},
     year = {2015},
     volume = {23},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a2/}
}
TY  - JOUR
AU  - V. V. Beniash-Kryvets
AU  - I. O. Govorushko
TI  - Representation varieties of finite index subgroups of Baumslag–Solitar groups
JO  - Trudy Instituta matematiki
PY  - 2015
SP  - 24
EP  - 28
VL  - 23
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a2/
LA  - ru
ID  - TIMB_2015_23_2_a2
ER  - 
%0 Journal Article
%A V. V. Beniash-Kryvets
%A I. O. Govorushko
%T Representation varieties of finite index subgroups of Baumslag–Solitar groups
%J Trudy Instituta matematiki
%D 2015
%P 24-28
%V 23
%N 2
%U http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a2/
%G ru
%F TIMB_2015_23_2_a2

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

Representation varieties of finite index subgroups of Baumslag–Solitar groups are investigated. It is proved that all irreducible components of the representation variety of a finite index subgroup of a Baumslag–Solitar group are birational isomorphic to irreducible components of the representation variety of some another Baumslag–Solitar group.

[1] Lubotzky A., Magid A., “Varieties of representations of finitely generated groups”, Memoirs AMS, 58, no. 336, 1985, 1–116 | DOI | MR

[2] Rudnick Z., “Representation varieties of solvable groups”, J. Pure and Applied Algebra, 45 (1987), 261–272 | DOI | MR | Zbl

[3] Benyash-Krivetz V. V., Rapinchuk A. S., Chernousov V. I., “Representation varieties of the fundamental groups of compact orientable surfaces”, Israel J. Math, 93 (1996), 29–71 | DOI | MR | Zbl

[4] Benyash-Krivets V. V., Chernousov V. I., “Mnogoobraziya predstavlenii fundamentalnykh grupp kompaktnykh neorientiruemykh poverkhnostei”, Mat. sb., 188:7 (1997), 47–92 | DOI | MR | Zbl

[5] Baumslag G., Solitar D., “Some two-generator one-relator non-hopfian groups”, Bull. AMS, 68:3 (1962), 199–201 | DOI | MR | Zbl

[6] Meskin S., “Nonresidually finite one-relator groups”, Trans. of the Amer. Math. Soc., 164 (1972), 105–114 | DOI | MR | Zbl

[7] Dudkin F. A., “Podgruppy konechnogo indeksa v gruppakh Baumslaga–Solitera”, Algebra i logika, 49:3 (2010), 331–345 | MR | Zbl

[8] Dudkin F. A., “Neprivodimye predstavleniya podgrupp konechnogo indeksa grupp Baumslaga–Solitera”, Sib. mat. zhurn., 54:6 (2013), 1273–1279 | MR | Zbl

[9] Benyash-Krivets V. V., Govorushko I. O., “O mnogoobraziyakh predstavlenii grupp Baumslaga–Solitera”, Vestnik BGU, ser. 1, 2014, no. 2, 43–45

[10] Benyash-Krivets V. V., Govorushko I. O., “O ratsionalnosti neprivodimykh komponent mnogoobrazii predstavlenii grupp Baumslaga–Solitera”, Vestnik BGU, ser. 1, 2015, no. 2, 88–91 | MR

[11] Gantmakher F. R., Teoriya matrits, Nauka, M., 1967 | MR

[12] Clay M., Forester V., “On the isomorphism problem for generalized Baumslag–Solitar groups”, Algebraic and Geometric Topology, 2008, no. 8, 2289–2322 | DOI | MR | Zbl