# zbMATH — the first resource for mathematics

Compute Distance To:
 Author ID: troitskii.evgenii-vadimovich Published as: Troitskii, E.; Troitskii, E. V.; Troitskij, E. V.; Troitsky, E.; Troitsky, E. V.; Troitsky, Evgenii V.; Troitsky, Evgenij; Troitsky, Evgenij V. Homepage: http://mech.math.msu.su/~troitsky/start_en.html External Links: Math-Net.Ru · ResearchGate · GND
 Documents Indexed: 64 Publications since 1985, including 5 Books
all top 5

#### Co-Authors

 33 single-authored 12 Fel’shtyn, Alexander 7 Manuĭlov, Vladimir Markovich 5 Frank, Michael 3 Mishchenko, Aleksandr Sergeevich 3 Nistor, Victor 3 Pavlov, Alexander A. 3 Solov’ëv, Yuriĭ Petrovich 1 Bojarski, Bogdan 1 Bolibrukh, Andreĭ Andreevich 1 Burghelea, Dan 1 Indukaev, Fedor 1 Irmatov, Anwar A. 1 Leonov, Yu. G. 1 Luchnikov, N. 1 Lupanov, Oleg Borisovich 1 Melrose, Richard Burt 1 Mishchenko, Evgeniĭ Frolovich 1 Popelenskii, Fedor Yu. 1 Postnikov, Mikhail Mikhaĭlovich 1 Vershik, Anatoliĭ Moiseevich 1 Weber, Andrzej 1 Zelikin, Mikhail Il’ich 1 Zietek, Malwina
all top 5

#### Serials

 7 Russian Journal of Mathematical Physics 7 Journal of Mathematical Sciences (New York) 4 Moscow University Mathematics Bulletin 4 Russian Mathematical Surveys 4 Functional Analysis and its Applications 2 Journal für die Reine und Angewandte Mathematik 2 Translations of Mathematical Monographs 2 Journal of $$K$$-Theory 2 Trends in Mathematics 1 Communications in Algebra 1 Journal of Mathematical Analysis and Applications 1 Studia Mathematica 1 Advances in Mathematics 1 Geometriae Dedicata 1 Mathematics of the USSR. Izvestiya 1 Proceedings of the American Mathematical Society 1 Soviet Mathematics. Doklady 1 Transactions of the American Mathematical Society 1 Zeitschrift für Analysis und ihre Anwendungen 1 Acta Applicandae Mathematicae 1 Annals of Global Analysis and Geometry 1 Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika 1 Zapiski Nauchnykh Seminarov POMI 1 The New York Journal of Mathematics 1 Mathematical Research Letters 1 Journal of Group Theory 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
all top 5

#### Fields

 42 Functional analysis (46-XX) 17 Global analysis, analysis on manifolds (58-XX) 16 Group theory and generalizations (20-XX) 13 Algebraic topology (55-XX) 13 Manifolds and cell complexes (57-XX) 10 $$K$$-theory (19-XX) 10 Dynamical systems and ergodic theory (37-XX) 9 Topological groups, Lie groups (22-XX) 9 Operator theory (47-XX) 5 Abstract harmonic analysis (43-XX) 3 Partial differential equations (35-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Category theory; homological algebra (18-XX) 2 General topology (54-XX) 1 General algebraic systems (08-XX) 1 Algebraic geometry (14-XX)

#### Citations contained in zbMATH

37 Publications have been cited 231 times in 116 Documents Cited by Year
Hilbert $$C^*$$-modules. Translated from the Russian by the authors. Zbl 1074.46001
Manuilov, V. M.; Troitsky, E. V.
2005
Twisted conjugacy classes in saturated weakly branch groups. Zbl 1192.20018
Fel’shtyn, Alexander; Leonov, Yuriy; Troitsky, Evgenij
2008
Twisted Burnside-Frobenius theory for discrete groups. Zbl 1204.20031
Fel’shtyn, Alexander; Troitsky, Evgenij
2007
Aspects of the property $$R_\infty$$. Zbl 1345.20038
Fel’shtyn, Alexander; Troitsky, Evgenij
2015
Hilbert $$C^*$$ and $$W^*$$-modules and their morphisms. Zbl 0968.46041
Manuilov, V. M.; Troitsky, E. V.
2000
Twisted Burnside theorem for type $$\text{II}_1$$ groups: an example. Zbl 1143.20026
Fel’shtyn, Alexander; Troitsky, Evgenij; Vershik, Anatoly
2006
Geometry of Reidemeister classes and twisted Burnside theorem. Zbl 1215.22003
Fel’shtyn, Alexander; Troitsky, Evgenij
2008
An index for gauge-invariant operators and the Dixmier-Douady invariant. Zbl 1030.46095
Nistor, Victor; Troitsky, Evgenij
2004
$$C^*$$-algebras and elliptic operators in differential topology. Transl. from the Russian by E. V. Troitsky. Zbl 0958.46038
Solovyov, Yu. P.; Troitsky, E. V.
2001
A twisted Burnside theorem for countable groups and Reidemeister numbers. Zbl 1147.20036
Fel’shtyn, Alexander; Troitsky, Evgenij
2006
Quantization of branched coverings. Zbl 1254.46064
Pavlov, A. A.; Troitskii, E. V.
2011
Noncommutative Riesz theorem and weak Burnside type theorem on twisted conjugacy. Zbl 1149.43004
Troitsky, E. V.
2006
On conditional expectations arising from group actions. Zbl 0903.46064
Frank, M.; Manuilov, V. M.; Troitsky, E. V.
1997
Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups. Zbl 06888112
Fel’shtyn, A. L.; Troitsky, E. V.
2018
Reidemeister classes and twisted inner representations. Zbl 1346.20036
Fel’shtyn, A.; Luchnikov, N.; Troitsky, E.
2015
Hilbert $$C^*$$-modules from group actions: beyond the finite orbits case. Zbl 1210.46044
Frank, Michael; Manuilov, Vladimir; Troitsky, Evgenij
2010
The index of equivariant elliptic operators over $$C^*$$-algebras. Zbl 0656.46043
Troitsky, E. V.
1987
Twisted Burnside theorem for two-step torsion-free nilpotent groups. Zbl 1143.20018
Fel’shtyn, Alexander; Indukaev, Fedor; Troitsky, Evgenij
2008
Discrete groups actions and corresponding modules. Zbl 1113.46058
Troitsky, E. V.
2003
Analysis of gauge-equivariant complexes and a topological index theorem for gauge-invariant families. Zbl 1318.19008
Nistor, V.; Troitsky, E.
2015
The Thom isomorphism in gauge-equivariant $$K$$-theory. Zbl 1139.58016
Nistor, Victor; Troitsky, Evgenij
2006
Orthogonal complements and endomorphisms of Hilbert modules and $$C^*$$-elliptic complexes. Zbl 0958.46031
Troitsky, Evgenii V.
1995
Reidemeister classes in lamplighter-type groups. Zbl 07098071
Troitsky, Evgenij
2019
A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras. Zbl 1228.46053
Frank, Michael; Manuilov, Vladimir; Troitsky, Evgenij
2010
A $$C^{*}$$-analogue of Kazhdan’s property (T). Zbl 1130.46036
Pavlov, A. A.; Troitsky, E. V.
2007
‘Twice’ equivariant $$C^*$$-index theorem and the index theorem for families. Zbl 1013.46059
Troitsky, Evgenij V.
2001
Lefschetz numbers and geometry of operators in $$W^*$$-modules. Zbl 0922.58081
Frank, M.; Troitskij, E. V.
1996
Lefschetz numbers of $$C^*$$-complexes. Zbl 0768.46040
Troitskij, E. V.
1991
Reidemeister classes in some weakly branch groups. Zbl 07073127
Troitsky, E. V.
2019
Manuilov algebra, $$C^\ast$$-Hilbert modules, and Kuiper type theorems. Zbl 1415.46038
Troitskii, E.
2018
Property (T) for topological groups and $$C^*$$-algebras. Zbl 1188.46032
Pavlov, A.; Troitsky, E.
2009
Twisted Burnside-Frobenius theory for virtually polycyclic groups. Zbl 1178.20038
Fel’shtyn, Alexander; Troitsky, Evgenij
2008
Conditional expectations of finite index and properties of modules arising from group actions. Zbl 1086.46040
Troitsky, E. V.
2004
Geometry and topology of operators on Hilbert $$C^*$$-modules. Zbl 0959.46043
Troitsky, E. V.
2000
Functionals on $$\ell_2(A)$$, Kuiper and Dixmier-Douady type theorems for $$C^*$$-Hilbert modules. Zbl 0987.46048
Troitskij, E. V.
1999
The Hirzebruch operator on piecewise linear manifolds and highest signatures. Zbl 0824.57019
Troitskij, E. V.
1993
The equivariant index of C *-elliptic operators. Zbl 0641.46047
Troitskij, E. V.
1987
Reidemeister classes in lamplighter-type groups. Zbl 07098071
Troitsky, Evgenij
2019
Reidemeister classes in some weakly branch groups. Zbl 07073127
Troitsky, E. V.
2019
Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups. Zbl 06888112
Fel’shtyn, A. L.; Troitsky, E. V.
2018
Manuilov algebra, $$C^\ast$$-Hilbert modules, and Kuiper type theorems. Zbl 1415.46038
Troitskii, E.
2018
Aspects of the property $$R_\infty$$. Zbl 1345.20038
Fel’shtyn, Alexander; Troitsky, Evgenij
2015
Reidemeister classes and twisted inner representations. Zbl 1346.20036
Fel’shtyn, A.; Luchnikov, N.; Troitsky, E.
2015
Analysis of gauge-equivariant complexes and a topological index theorem for gauge-invariant families. Zbl 1318.19008
Nistor, V.; Troitsky, E.
2015
Quantization of branched coverings. Zbl 1254.46064
Pavlov, A. A.; Troitskii, E. V.
2011
Hilbert $$C^*$$-modules from group actions: beyond the finite orbits case. Zbl 1210.46044
Frank, Michael; Manuilov, Vladimir; Troitsky, Evgenij
2010
A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras. Zbl 1228.46053
Frank, Michael; Manuilov, Vladimir; Troitsky, Evgenij
2010
Property (T) for topological groups and $$C^*$$-algebras. Zbl 1188.46032
Pavlov, A.; Troitsky, E.
2009
Twisted conjugacy classes in saturated weakly branch groups. Zbl 1192.20018
Fel’shtyn, Alexander; Leonov, Yuriy; Troitsky, Evgenij
2008
Geometry of Reidemeister classes and twisted Burnside theorem. Zbl 1215.22003
Fel’shtyn, Alexander; Troitsky, Evgenij
2008
Twisted Burnside theorem for two-step torsion-free nilpotent groups. Zbl 1143.20018
Fel’shtyn, Alexander; Indukaev, Fedor; Troitsky, Evgenij
2008
Twisted Burnside-Frobenius theory for virtually polycyclic groups. Zbl 1178.20038
Fel’shtyn, Alexander; Troitsky, Evgenij
2008
Twisted Burnside-Frobenius theory for discrete groups. Zbl 1204.20031
Fel’shtyn, Alexander; Troitsky, Evgenij
2007
A $$C^{*}$$-analogue of Kazhdan’s property (T). Zbl 1130.46036
Pavlov, A. A.; Troitsky, E. V.
2007
Twisted Burnside theorem for type $$\text{II}_1$$ groups: an example. Zbl 1143.20026
Fel’shtyn, Alexander; Troitsky, Evgenij; Vershik, Anatoly
2006
A twisted Burnside theorem for countable groups and Reidemeister numbers. Zbl 1147.20036
Fel’shtyn, Alexander; Troitsky, Evgenij
2006
Noncommutative Riesz theorem and weak Burnside type theorem on twisted conjugacy. Zbl 1149.43004
Troitsky, E. V.
2006
The Thom isomorphism in gauge-equivariant $$K$$-theory. Zbl 1139.58016
Nistor, Victor; Troitsky, Evgenij
2006
Hilbert $$C^*$$-modules. Translated from the Russian by the authors. Zbl 1074.46001
Manuilov, V. M.; Troitsky, E. V.
2005
An index for gauge-invariant operators and the Dixmier-Douady invariant. Zbl 1030.46095
Nistor, Victor; Troitsky, Evgenij
2004
Conditional expectations of finite index and properties of modules arising from group actions. Zbl 1086.46040
Troitsky, E. V.
2004
Discrete groups actions and corresponding modules. Zbl 1113.46058
Troitsky, E. V.
2003
$$C^*$$-algebras and elliptic operators in differential topology. Transl. from the Russian by E. V. Troitsky. Zbl 0958.46038
Solovyov, Yu. P.; Troitsky, E. V.
2001
‘Twice’ equivariant $$C^*$$-index theorem and the index theorem for families. Zbl 1013.46059
Troitsky, Evgenij V.
2001
Hilbert $$C^*$$ and $$W^*$$-modules and their morphisms. Zbl 0968.46041
Manuilov, V. M.; Troitsky, E. V.
2000
Geometry and topology of operators on Hilbert $$C^*$$-modules. Zbl 0959.46043
Troitsky, E. V.
2000
Functionals on $$\ell_2(A)$$, Kuiper and Dixmier-Douady type theorems for $$C^*$$-Hilbert modules. Zbl 0987.46048
Troitskij, E. V.
1999
On conditional expectations arising from group actions. Zbl 0903.46064
Frank, M.; Manuilov, V. M.; Troitsky, E. V.
1997
Lefschetz numbers and geometry of operators in $$W^*$$-modules. Zbl 0922.58081
Frank, M.; Troitskij, E. V.
1996
Orthogonal complements and endomorphisms of Hilbert modules and $$C^*$$-elliptic complexes. Zbl 0958.46031
Troitsky, Evgenii V.
1995
The Hirzebruch operator on piecewise linear manifolds and highest signatures. Zbl 0824.57019
Troitskij, E. V.
1993
Lefschetz numbers of $$C^*$$-complexes. Zbl 0768.46040
Troitskij, E. V.
1991
The index of equivariant elliptic operators over $$C^*$$-algebras. Zbl 0656.46043
Troitsky, E. V.
1987
The equivariant index of C *-elliptic operators. Zbl 0641.46047
Troitskij, E. V.
1987
all top 5

#### Cited by 124 Authors

 9 Journal of Mathematical Analysis and Applications 9 Journal of Functional Analysis 7 Russian Journal of Mathematical Physics 6 Journal of Mathematical Sciences (New York) 5 Transactions of the American Mathematical Society 4 Topology and its Applications 4 Linear Algebra and its Applications 3 Communications in Algebra 3 Advances in Mathematics 3 Geometriae Dedicata 3 Journal of Algebra 3 Positivity 3 Journal of Algebra and its Applications 2 Communications in Mathematical Physics 2 Linear and Multilinear Algebra 2 Journal of Geometry and Physics 2 Algebra and Logic 2 Functional Analysis and its Applications 2 Annals of Global Analysis and Geometry 2 International Journal of Mathematics 2 Expositiones Mathematicae 2 Journal of Group Theory 2 Banach Journal of Mathematical Analysis 2 Annals of Functional Analysis 1 Annales de l’Institut Fourier 1 Bulletin of the London Mathematical Society 1 Compositio Mathematica 1 Integral Equations and Operator Theory 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Zeitschrift 1 Proceedings of the American Mathematical Society 1 Siberian Mathematical Journal 1 Ergodic Theory and Dynamical Systems 1 Acta Applicandae Mathematicae 1 $$K$$-Theory 1 International Journal of Algebra and Computation 1 Differential Geometry and its Applications 1 Bulletin of the American Mathematical Society. New Series 1 Indagationes Mathematicae. New Series 1 Journal of Knot Theory and its Ramifications 1 Topological Methods in Nonlinear Analysis 1 Transformation Groups 1 Geometry & Topology 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Journal of the Institute of Mathematics of Jussieu 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 Journal of Fixed Point Theory and Applications 1 Complex Analysis and Operator Theory 1 Groups, Geometry, and Dynamics 1 Journal of Modern Dynamics 1 Journal of Topology and Analysis 1 Journal of $$K$$-Theory
 69 Functional analysis (46-XX) 38 Group theory and generalizations (20-XX) 27 Operator theory (47-XX) 21 Algebraic topology (55-XX) 17 Dynamical systems and ergodic theory (37-XX) 16 Global analysis, analysis on manifolds (58-XX) 14 Topological groups, Lie groups (22-XX) 10 $$K$$-theory (19-XX) 9 Manifolds and cell complexes (57-XX) 6 Abstract harmonic analysis (43-XX) 5 Differential geometry (53-XX) 3 Algebraic geometry (14-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Partial differential equations (35-XX) 3 General topology (54-XX) 2 Associative rings and algebras (16-XX) 2 Category theory; homological algebra (18-XX) 2 Probability theory and stochastic processes (60-XX) 1 Combinatorics (05-XX) 1 General algebraic systems (08-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX)