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Benyash-Krivets, Valerii Vatslavovich

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Total publications: 16
Scientific articles: 13

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Abstract pages:4411
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References:366
Professor
Doctor of physico-mathematical sciences (2001)
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A number of papers (with A. S. Rapinchuk and V. I. Chernousov) were devoted to an investigation of representation varieties $R_n(\Gamma)$ and character varieties $X_n(\Gamma)$ for some classes of finitely generated groups, in particular, for fundamental groups of compact surfaces. It is proved that if $\Gamma=\Delta_g$ is a fundamental group of a compact orientable surface of genus $g$, then $R_n(\Delta_g)$ is an irreducible $\mathbb{Q}$-rational variety for all $n$ and $g$. It is obtained a full description of representation and character varieties of fundamental groups $\G_g$ of compact non-orentable surfaces. Developed methods were used for description of $n$-dimensional representation and character varieties both of wide class of groups with one relation and several groups of $F$-type. The problem of decomposing finitely generated groups into non trivial free product with amalgamation is investigated in a number of papers. It is proved that a group with two generators and one relation with torsion is a non trivial free product with amalgamation. Decomposing generalized triangle groups is investigated. As a corollary we proved that Fuchsian groups $H_1=\langle a,b\mid [a,b]^n=1\rangle$ and $H_2=\langle a,b\mid a^2=[a,b]^n=1\rangle$, where $n\ge2$, are non trivial free products with amalgamation. It is proved that if the dimension of a character variety of representations of a finitely generated group $\Gamma$ into $SL_2(\mathbb{C})$ is greater than 1 then $\Gamma$ is a non trivial free product with amalgamation.

Biography

Graduated fromFaculty of Mathematics and Mechanics of Byelorussian State University in 1983 (department of algebra). Ph.D. thesis was defended in 1989. D.Sci. thesis was defended in 2001. A list of my work contains more than 40 titles.


http://www.mathnet.ru/eng/person8529
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
2019
1. V. V. Beniash-Kryvets, Y. A. Yushkevich, “On the Tits alternative for generalized tetraedron groups of type $(2, 2, N, 2, 2, 2)$”, PFMT, 2019, 2(39),  54–60  mathnet
2018
2. N. A. Izobov, V. V. Gorokhovik, Yu. S. Kharin, L. A. Yanovich, D. F. Bazylev, V. V. Benyash-Krivets, I. D. Suprunenko, S. V. Tikhonov, “V. I . Yanchevskii is 70”, Algebra Discrete Math., 26:1 (2018),  C–F  mathnet
2016
3. A. N. Admiralova, V. V. Beniash-Krivets, “On linear groups with the property of order finiteness of all primitive words in generators”, Fundam. Prikl. Mat., 21:1 (2016),  23–35  mathnet; J. Math. Sci., 233:5 (2018), 616–625
4. V. V. Benyash-Krivets, I. O. Govorushko, “Representation and character varieties of the Baumslag–Solitar groups”, Tr. Mat. Inst. Steklova, 292 (2016),  26–42  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 292 (2016), 20–36  isi  scopus
2015
5. V. V. Beniash-Kryvets, I. O. Govorushko, “Representation varieties of finite index subgroups of Baumslag–Solitar groups”, Tr. Inst. Mat., 23:2 (2015),  24–28  mathnet
2009
6. V. V. Benyash-Krivets, V. P. Platonov, “Groups of $S$-units in hyperelliptic fields and continued fractions”, Mat. Sb., 200:11 (2009),  15–44  mathnet  mathscinet  zmath  elib; Sb. Math., 200:11 (2009), 1587–1615  isi  elib  scopus
2008
7. V. V. Benyash-Krivets, V. P. Platonov, “Continued fractions and $S$-units in hyperelliptic fields”, Uspekhi Mat. Nauk, 63:2(380) (2008),  159–160  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:2 (2008), 357–359  isi  elib  scopus
2007
8. V. V. Benyash-Krivets, V. P. Platonov, “$S$-units in hyperelliptic fields”, Uspekhi Mat. Nauk, 62:4(376) (2007),  149–150  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 62:4 (2007), 784–786  isi  elib  scopus
2001
9. V. V. Benyash-Krivets, “Decomposing finitely generated groups into free products with amalgamation”, Mat. Sb., 192:2 (2001),  3–26  mathnet  mathscinet  zmath; Sb. Math., 192:2 (2001), 163–186  isi  scopus
1998
10. V. V. Benyash-Krivets, “Decomposing one-relator products of cyclic groups into free products with amalgamation”, Mat. Sb., 189:8 (1998),  13–26  mathnet  mathscinet  zmath; Sb. Math., 189:8 (1998), 1125–1137  isi  scopus
1997
11. V. V. Benyash-Krivets, V. I. Chernousov, “Representation varieties of the fundamental groups of non-orientable surfaces”, Mat. Sb., 188:7 (1997),  47–92  mathnet  mathscinet  zmath; Sb. Math., 188:7 (1997), 997–1039  isi  scopus
1990
12. V. P. Platonov, V. V. Benyash-Krivets, “Character rings of representations of finitely generated groups”, Trudy Mat. Inst. Steklov., 183 (1990),  169–178  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 183 (1991), 203–213
1986
13. V. P. Platonov, V. V. Benyash-Krivets, “Rings of characters of $n$-dimensional representations of finitely generated groups”, Dokl. Akad. Nauk SSSR, 289:2 (1986),  293–297  mathnet  mathscinet  zmath

2015
14. S. I. Adian, V. V. Benyash-Krivets, V. M. Buchstaber, E. I. Zel'manov, V. V. Kozlov, G. A. Margulis, S. P. Novikov, A. N. Parshin, G. Prasad, A. S. Rapinchuk, L. D. Faddeev, V. I. Chernousov, “Vladimir Petrovich Platonov (to the 75 anniversary since the birth of)”, Chebyshevskii Sb., 16:4 (2015),  6–10  mathnet
15. S. I. Adian, V. V. Benyash-Krivets, V. M. Buchstaber, E. I. Zelmanov, V. V. Kozlov, G. A. Margulis, S. P. Novikov, A. N. Parshin, G. Prasad, A. S. Rapinchuk, L. D. Faddeev, V. I. Chernousov, “Vladimir Petrovich Platonov (on his 75th birthday)”, Uspekhi Mat. Nauk, 70:1(421) (2015),  204–207  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 70:1 (2015), 197–201  isi
2010
16. V. V. Benyash-Krivets, A. B. Zhizhchenko, E. I. Zel'manov, A. A. Mal'tsev, G. A. Margulis, S. P. Novikov, Yu. S. Osipov, G. Prasad, A. S. Rapinchuk, L. D. Faddeev, “Vladimir Petrovich Platonov (on his 70th birthday)”, Uspekhi Mat. Nauk, 65:3(393) (2010),  203–206  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 65:3 (2010), 593–596  isi

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