Persons: Troitskii, Evgenij Vadimovich

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Troitskii, Evgenij Vadimovich

Professor

Doctor of physico-mathematical sciences (1993)

Speciality:

01.01.04 (Geometry and topology)

Birth date:

13.02.1961

E-mail:

Website:

https://mech.math.msu.su/~troitsky https://istina.msu.ru/profile/e.v.troitsky

Keywords:

index of elliptic operator, $C^*$-algebra, $C^*$-Hilbert module, dynamical system, conditional expectation, irreducible representation, Reidemeister number.

UDC:

517.98, 512.7, 517.986

Subject:

Noncommutative Geometry, Algebraic and Differential Topology, Functional Analysis, $K$-theory of $C^*$-algebras, index theory of elliptic operators, Noncommutative Harmonic Analysis, Group Theory.

Main publications:

Troitsky E., “Geometric essence of “compact” operators on Hilbert C*-modules”, Journal of Mathematical Analysis and Applications, 485 (2020), 123842
Felshtyn A., Troitsky E., “Twisted Burnside-Frobenius theory for discrete groups”, J. Reine Angew. Math. (Crelle's journal), 613 (2007), 193–210
Pavlov A.A., Troitsky E.V., “A $C^*$-analogue of Kazhdan's property (T)”, Adv. in Math., 216 (2007), 75–88
Manuilov V.M., Troitsky E.V., Hilbert $C^*$-modules, AMS, Providence, RI, 2005
Nistor V., Troitsky E., “An index for gauge-invariant operators and the Dixmier-Douady invariant”, Trans. Amer. Math. Soc., 356:1 (2004), 185–218

https://www.mathnet.ru/eng/person18446

List of publications on Google Scholar

https://zbmath.org/authors/ai:troitskij.evgenij-vadimovich

https://mathscinet.ams.org/mathscinet/MRAuthorID/223790

ISTINA

https://istina.msu.ru/workers/2319593

	Publications in Math-Net.Ru	Citations
	2023
1.	E. V. Troitsky, “Reidemeister Classes, Wreath Products, and Solvability”, Mat. Zametki, 114:6 (2023), 949–953 ; Math. Notes, 114:6 (2023), 1494–1498
2.	E. V. Troitskii, “Reidemeister Classes in Some Lamplighter-Type Groups”, Mat. Zametki, 113:4 (2023), 626–630 ; Math. Notes, 113:4 (2023), 605–609	2
	2020
3.	E. V. Troitskii, D. V. Fufaev, “Compact Operators and Uniform Structures in Hilbert $C^*$-Modules”, Funktsional. Anal. i Prilozhen., 54:4 (2020), 74–84 ; Funct. Anal. Appl., 54:4 (2020), 287–294	4
	2016
4.	E. V. Troitskii, “Two examples related to the twisted Burnside–Frobenius theory for infinitely generated groups”, Fundam. Prikl. Mat., 21:5 (2016), 219–227 ; J. Math. Sci., 248:5 (2020), 661–666	2
	2007
5.	A. A. Pavlov, E. V. Troitskii, “Property (T) for topological groups and $C^*$-algebras”, Fundam. Prikl. Mat., 13:8 (2007), 171–192 ; J. Math. Sci., 159:6 (2009), 863–878	1
	2006
6.	E. V. Troitskii, “Noncommutative Riesz Theorem and Weak Burnside Type Theorem on Twisted Conjugacy”, Funktsional. Anal. i Prilozhen., 40:2 (2006), 44–54 ; Funct. Anal. Appl., 40:2 (2006), 117–125	14
	2000
7.	E. V. Troitskii, “Thom isomorphism in the “twice” equivariant $K$-theory of $C^*$-fibrations”, Zap. Nauchn. Sem. POMI, 266 (2000), 245–253 ; J. Math. Sci. (N. Y.), 113:5 (2003), 683–688
	1999
8.	E. V. Troitskii, “Actions of compact groups on algebras, the $C^*$-index theorem, and families”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 68 (1999), 129–188 ; J. Math. Sci. (New York), 105:2 (2001), 1884–1923
9.	E. V. Troitskii, “Functionals on $l_2(A)$, Kuiper and Dixmier–Douady Type Theorems for $C^*$-Hilbert Modules”, Trudy Mat. Inst. Steklova, 225 (1999), 362–380 ; Proc. Steklov Inst. Math., 225 (1999), 344–362
	1998
10.	V. M. Manuilov, E. V. Troitskii, M. Frank, “Actions of groups and conditional expectations of finite index”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1998, no. 2, 30–34
	1996
11.	E. V. Troitskii, M. Frank, “Lefschetz Numbers and Geometry of Operators in $W^*$-Modules”, Funktsional. Anal. i Prilozhen., 30:4 (1996), 45–57 ; Funct. Anal. Appl., 30:4 (1996), 257–266	7
	1994
12.	E. V. Troitskii, “An Averaging Theorem in $C^*$-Hilbert Modules and Operators without Adjoint”, Funktsional. Anal. i Prilozhen., 28:3 (1994), 88–92 ; Funct. Anal. Appl., 28:3 (1994), 220–223
	1993
13.	E. V. Troitskii, “The Hirzebruch operator on piecewise linear manifolds and highest signatures”, Uspekhi Mat. Nauk, 48:1(289) (1993), 189–190 ; Russian Math. Surveys, 48:1 (1993), 197–198
14.	E. V. Troitskii, “Traces, $C^*$-elliptic complexes, and higher-dimension even cyclic homology”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1993, no. 5, 36–39
	1992
15.	E. V. Troitskii, “An exact formula for the index of an equivariant $C^*$-elliptic operator”, Trudy Mat. Inst. Steklov., 193 (1992), 178–182 ; Proc. Steklov Inst. Math., 193 (1993), 197–201
	1989
16.	E. V. Troitskii, “Exact $K$-cohomological $C^*$-index formula. II. The index theorem and its applications”, Uspekhi Mat. Nauk, 44:1(265) (1989), 213–214 ; Russian Math. Surveys, 44:1 (1989), 259–260
	1988
17.	E. V. Troitskii, “An exact $K$-cohomology $C^*$-index formula. I. Thom isomorphism and topological index”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1988, no. 2, 83–85
	1986
18.	E. V. Troitskii, “Contractibility of the full general linear group of the $l_2(A)$”, Funktsional. Anal. i Prilozhen., 20:4 (1986), 58–64 ; Funct. Anal. Appl., 20:4 (1986), 301–307	3
19.	E. V. Troitskii, “The equivariant index of $C^*$-elliptic operators”, Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986), 849–865 ; Math. USSR-Izv., 29:1 (1987), 207–224	4
	1985
20.	E. V. Troitskii, “The index theorem for equivariant $C^*$-elliptic operators”, Dokl. Akad. Nauk SSSR, 282:5 (1985), 1059–1061
21.	E. V. Troitskii, “On the connection between complex and operator topological equivariant $K$-theories”, Uspekhi Mat. Nauk, 40:4(244) (1985), 227–228 ; Russian Math. Surveys, 40:4 (1985), 243–244
22.	E. V. Troitskii, “Classifying spaces for a $K$-functor connected with a $C^*$-algebra”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1985, no. 1, 96–98	2

	2004
23.	V. V. Belokurov, A. A. Egorov, A. S. Mishchenko, F. Yu. Popelenskii, V. A. Sadovnichii, E. V. Troitskii, A. T. Fomenko, E. T. Shavgulidze, “Yurii Petrovich Solov'ev (obituary)”, Uspekhi Mat. Nauk, 59:5(359) (2004), 135–140 ; Russian Math. Surveys, 59:5 (2004), 941–947	2
	2001
24.	A. A. Bolibrukh, A. A. Irmatov, M. I. Zelikin, O. B. Lupanov, V. M. Maynulov, E. F. Mishchenko, M. M. Postnikov, Yu. P. Solov'ev, E. V. Troitskii, “Aleksandr Sergeevich Mishchenko (on his 60th birthday)”, Uspekhi Mat. Nauk, 56:6(342) (2001), 167–170 ; Russian Math. Surveys, 56:6 (2001), 1187–1191	2
25.	A. A. Irmatov, O. B. Lupanov, V. P. Maslov, V. M. Manuilov, A. A. Mikhalev, V. A. Sadovnichii, Yu. P. Solov'ev, E. V. Troitskii, A. T. Fomenko, “Aleksandr Sergeevitch Mischenko”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2001, no. 5, 67–69	1

Presentations in Math-Net.Ru

1.	$C^$-Fredholm operators and polar decomposition type properties E. V. Troitskii Algebras in Analysis* March 31, 2023 18:00
2.	Geometric essence of “compact” operators on Hilbert $C^$-modules E. V. Troitskii Algebras in Analysis* April 5, 2019 18:05
3.	Классы Райдемайстера: алгебра, геометрия и анализ E. V. Troitskii Meetings of the St. Petersburg Mathematical Society December 13, 2011 18:00
4.	Algebra, geometry and analysis connected with Reidemeister classes E. V. Troitskii P.K. Rashevskii seminar on tensor and vector analysis with applications in geometry, mechanics and physics October 10, 2011 18:30
5.	От теоремы Атьи–Зингера к крученой $K$-теории E. V. Troitskii Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS April 23, 2009 11:00
6.	Классы Райдемайстера: алгебра, геометрия и анализ E. V. Troitskii Seminar by Algebra Department May 20, 2008 15:00

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