Research Interests:
- Theory of C*-algebras, Hilbert C*-modules and operators on them
[1], [2], [3], [4], [5], [6], [7], [8], [9], [12], [13], [14], [15], [16], [19], [21], [22], [24], [25], [31],
[38], [40], [42],
[47],[48],
[49],
- C*-conditional expectations. [19], [31],
[49],
- Discrete and non-commutative dynamics. [9], [31],
[47],
- Topological dynamics. [36],
[38], [41],
[42],
[44],
[45],
[46],
- Index theory of elliptic operators <[3], [4], [6], [7], [8], [10], [21], [29], [33], [52],
- Theory of Banach categories. [1], [2], [21], [33],
[40],
- Non-commutative geometry, cyclic homology. [9], [15], [16], [20], [52],
- Algebraic topology (classifying spaces and spectral sequences). [1], [2], [23],
- Topological and operator K-theory. [1], [2], [3], [4], [6], [7], [8], [9], [10], [12], [15], [16], [21], [23], [29], [33],
[39], [52],
- Novikov Conjecture [11],
- Twisted K-theory.[33],
[39], [52],
- Mathematical physics (gauge theory) [36],
[39],[49],
[52],
- Group theory, harmonic analysis [36],
[37],
[38], [40], [41],
[42],
[43],
[44], [45],
[46], [50], [51],
Main Publications of Evgenij Troitsky up to 2015
(in inverse chronological order)
The publication list after 2015 is available at
the system ISTINA MSU
-
[52]
Nistor V., Troitsky E.
Analysis of gauge-equivariant complexes and a topological index theorem
for gauge-invariant families.
Russian Journal of Mathematical Physics
22 (2015) No. 1, 74-97.
Preprint MPIM 2015-9 (PDF)
-
[51]
Alexander Fel'shtyn, Evgenij Troitsky.
Aspects of the property R∞.
Journal of Group Theory
18 (2015)
Preprint MPIM 2014-28 (PDF)
-
[50] Fel’shtyn A., Luchnikov N., Troitsky E.
Reidemeister classes and twisted inner representations.
Russian Journal of Mathematical Physics 22 (2015) No. 3, 301-306.
Preprint MPIM 2014-27 (PDF)
-
[49]
Pavlov A.A., Troitskii E.V.
Quantization of branched coverings
Russian J. of Math. Phys. 18, N 3 (2011), 338-352.
Arxiv
-
[48]
Frank M., Manuilov V., Troitsky E.
A reflexivity criterion for Hilbert C*-modules over commutative C*-algebras
New York Journal of Mathematics 16 (2010), 399–408.
Arxiv
-
[47]
Frank M., Manuilov V., Troitsky E.
Hilbert C*-modules from group actions: beyond the finite orbits case
Studia Mathematica 200 (2010), 131–148.
Arxiv
-
[46]
Felshtyn A., Troitsky E.
Théorie de Burnside–Frobenius tordue pour les groupes
virtuellement polycycliques
C. R. Acad. Sci. Paris, Ser. I
346 (2008), 1033–1038.
-
[45]
Felshtyn A., Troitsky E.
Geometry of Reidemeister classes and twisted Burnside theorem.
J. K-Theory 2 (2008), 463-506.
(Preliminary version: PDF file )
- [44]
Felshtyn A., Leonov Yu., Troitsky E.
Twisted conjugacy classes in saturated weakly branch groups,
Geometriae Dedicata 134 (2008), 61-73.
http://arxiv.org/abs/math/0606725
- [43]
Felshtyn A., Indukaev F., Troitsky E.
Twisted Burnside theorem for two-step torsion-free nilpotent groups.
In: C*-algebras and elliptic theory. II.
(Proceedings of
Bedlewo'06 Conference,)
Birkhäuser Trends in Math. series, 2008, pp.87-101.
( PDF file of a preprint version)
-
[42]
Pavlov A.A., Troitsky E.V.
Property (T) for topological groups and C*-algebras.
Fundam. Prikl. Matem. 13 (2007),
171—192. (in Russian)
English translation:
Journal of Mathematical Sciences,
2009, Volume 159, Issue 6, pp 863-878.
- [41]
Felshtyn A., Troitsky E.
Twisted Burnside-Frobenius theory for discrete groups.
J. Reine Angew. Math. (Crelle's journal) 613 (2007), 193-210.
http://arxiv.org/abs/math/0606179
- [40]
Pavlov A.A., Troitsky E.V.
A C*-analogue of Kazhdan’s property (T).
Adv. in Math. 216 (2007), 75-88.
http://arxiv.org/abs/math/0606724
-
[39]
Nistor V., Troitsky E.
The Thom isomorphism in gauge-equivariant K-theory.
In: C*-algebras and elliptic theory
(Proceedings of
Bedlewo'04 Conference,)
Birkhäuser Trends in Math. series, 2006, pp.213-245.
( PDF file of a preprint version)
http://arxiv.org/abs/math/0506408
-
[38]
Troitsky E.
Noncommutative Riesz theorem
and weak Burnside type theorem on twisted conjugacy.
Funct. Anal. Prilozh. 40 (2006) no.2,
44-54
(In Russian, English translation: Funct. Anal. Appl.
40 (2006), No. 2, 117-125)
http://arxiv.org/abs/math/0606191
-
[37]
Felshtyn A., Troitsky E., Vershik A.
Twisted Burnside theorem for type II1
groups:
an example. Math. Res. Lett.
13 (2006)
No. 5, 719-728
http://arxiv.org/abs/math/0606161
-
[36]
Felshtyn A., Troitsky E.
A twisted Burnside theorem for countable groups and Reidemeister
numbers.
In: K.Consani and M.Marcolli, editors, Proc.
Workshop Noncommutative Geometry and Number Theory (Bonn, 2003)
Braunschweig, Vieweg, 2006, pp. 141-154.
(PDF file препринтной версии )
http://arxiv.org/abs/math/0606155
- [35] Manuilov V.M., Troitsky E.V. Hilbert C*-modules.
AMS, 2005 - 202 pp.
- [34] Alanya L.A., Gussein-Zade S.M., Dynnikov I.A.,
Manuilov V.M., Millionshchikov D.V., Mishchenko A.S., Morozova E.A., Panov
T.E., Postnikov M.M., Sklyarenko E.G., Smirnov Yu.M. (ed.), Troitsky E.V. Problem book in
analytical geometry and linear algebra. Second revised edition, Logos,
Moscow, 2005 (in Russian). - 376 pp.
-
[33]
Troitsky E.,
Nistor V.
An index for gauge-invariant operators and the Dixmier-Douady
invariant.
Trans. Amer. Math. Soc., 356 (2004) No.1, 185-218.
(
Preprint 009, Max-Planck-Institut für Mathematik,
feb. 2002. PDF file)
- [32] Veselov A.P., Troitsky E.V. Lectures in
Analytical Geometry. Second edition,
Lan' Press, St-Petersburg, 2003 (in Russian).
- [31] Troitsky E.V.
Discrete
groups actions and corresponding modules. Proc. Amer. Math. Soc.
131 (2003) No.11, 3411-3422. PDF file of a preliminary
version
- [30] Veselov A.P., Troitsky E.V. Lectures in
Analytical Geometry. Moscow Univ., 2002 (in Russian).
- [29] Troitsky E.V. ''Twice'' equivariant C*-index theorem
and the index theorem for families. Acta. Appl. Math. 68
(2001), 39-70.
- [28] Manuilov V.M., Troitsky E.V. Hilbert C*-modules.
Factorial Press, Moscow, 2001 (in Russian).
- [27] Alanya L.A., Gussein-Zade S.M., Dynnikov I.A.,
Manuilov V.M., Millionshchikov D.V., Mishchenko A.S., Morozova E.A., Panov
T.E., Postnikov M.M., Sklyarenko E.G., Smirnov Yu.M. (ed.), Troitsky E.V. Problem book in
analytical geometry and linear algebra. Moscow: Fizmatlit, 2001 (in
Russian)
- [26] Solovyov Yu.P., Troitsky E.V. C*-algebras and
elliptic operators in differential topology. (vol. 192 of
Translations of Mathemetical Monographs) Amer. Math. Soc, Providence,
RI, 2000 (Revised English translation).
- [25] Manuilov V.M., Troitsky E.V. Hilbert C*- and
W*-modules and their morphisms. J. Math. Sci. (N.Y.) 98
(2000), N 2, 137-201. PDF file of a preliminary
version
- [24] Troitsky E.V. Geometry and topology of operators on
Hilbert C*-modules. J. Math. Sci. (N.Y.) 98 (2000), N 2,
245-290. PDF file of a
preliminary version
- [23] Troitsky E.V.
Thom isomorphism in "twice" equivariant
K-theory of C*-bundles. Proceedings of Sci. Sem. of St-Petersb. Branch of
Steklov Inst. of Math. 266 (2000), 245-253.
(in Russian.
English translation:
Journal of Mathematical Sciences, 2003, Volume 113, Issue 5, pp 683-688
)
- [22] Troitsky E.V. Functionals on l2(A), Kuiper and
Dixmier-Douady type theorems for C*-Hilbert modules. Trudy Matem. Inst.
RAN im. V.A.Steklova 225 (1999), 362-380 (in Russian. English
translation: Proceedings Steklov Inst. Math. 1999, vol. 225, 344-362
) pdf file
- [21] Troitsky E.V. Actions of compact groups on algebras,
C*-index theorem and families Itogy nauki i tehniki. Ser. Modern
Mathematics and Its Applications. Thematical surveys. 68 (1999),
129-188 (in Russian. English translation:
Journal of Mathematical Sciences,
2001, Volume 105, Issue 2, pp 1884-1923). (E-print math.OA/9904002)
- [20] Troitsky E.V. Compact group actions on Hilbert
modules and C*-elliptic complexes. Tensor and Vector Analysis
(A.T.Fomenko, O.V.Manturov and V.V.Trofimov, eds.), Gordon and Breach
Sci. Publ., 1998, 251-281.
- [19] Frank M., Manuilov V., Troitsky E. Conditional
expectations arising from group actions. Z. Anal. Anwendungen 16
(1997) No. 4, 831-850. Preliminary version: pdf file
- [18] Solovyov Yu.P., Troitsky E.V. C*-algebras and
elliptic operators in differential topology. Moscow: Factorial Press,
1996. - 352 p. (in Russian).
- [17] Troitsky E.V. Degree of a map and
applications (Lectures). Moscow Univ., 1996. - 56 p. (in Russian). pdf file
- [16] Frank M., Troitsky E.
Lefschetz numbers and geometry
of operators in W*-modules. Func. Anal. i Pril. 30 (1996) No. 4,
45-57 (in Russian),
English translation: Funct. Anal. Appl.
30 (1996).
- [15] Troitsky E.V. Orthogonal complements and
endomorphisms of Hilbert modules and C*-elliptic complexes. Novikov
Conjectures, Index Theorems and Ridgidity, V.2 (London Math. Soc. Lect.
Notes Series V.227), 1995, P. 309-331. pdf file of preliminary
version.
- [14] Troitsky E.V.
An averaging theorem in C*-Hilbert
modules and operators without adjoint. Func. Anal. i Pril. 28 (1994)
No. 3, 88-92 (in Russian),
English translation: Funct. Anal.
Appl. 28 (1994).
- [13] Troitsky E.V. Some aspects of geometry of operators
in Hilbert modules. Preprint, Ruhr-Universitat Bochum, Fakultat fur
Mathematik, Bericht-Nr. 173, January, 1994, 19 P.
- [12] Troitsky E.V. Traces, C*-elliptic complexes and the
even cyclic homology. Vestnik Mosc. Univ. Ser. 1. Mat. Meh. 1993, N
5, 36-39 (in Russian), English translation: Moscow Univ. Math.
Bull. 48 (1993), No 5.
- [11] Troitsky E.V.
The Hirzebruch operator on the PL
manifolds and the higher signatures. Usp. Mat. Nauk. 48 (1993), No 1,
189-190 (in Russian),
English transl.: Russian Math. Surv.
48 (1993), No 1, 197-198.
- [10] Troitsky E.V.
An exact formula for the index of
equivariant C*-elliptic operator. Trudy Mat. Inst. Steklova. 193
(1992), 178-182. (in Russian),
English transl.: Proceedings of
Steklov Institute 1993, Issue 3, 197-201.
- [9] Troitsky E.V. Lefschetz numbers of C*-complexes.
Springer Lecture Notes in Math. V. 1474 (1991), 193-206.
- [8] Troitsky E.V.
Exact K-cohomological C*-index formula.
II: The index theorem and its applications.
Usp. Mat. Nauk. 44 (1989)
No 1, 213-214 (in Russian),
English translation: Sov. Math.
Surv. 44 (1989) No 1, 259-261.
- [7] Troitsky E.V. An exact K-cohomological C*-index
formula.I: The Thom isomorfism and the topological index. Vestn. Mosc.
Univ. Ser. 1. Math., Mekh. 1988, No 2, 83-85 (in Russian), English
translation: Moscow Univ. Math. Bull. 43 (1988) No 2, 57-60.
- [6] Troitsky E.V. The index of equivariant elliptic
operators over C*-algebras. Annals of Global Analysis and Geometry 5
(1987), N 1, 3-22.
- [5] Troitsky E.V.
Contractibility of the full general
linear group of the C*-Hilbert module l2(A). Func. Anal. i Pril. 20
(1986) No 4, 58-64 (in Russian),
English translation: Funct.
Anal. Appl. 20 (1986), No 4, 301-307.
- [4] Troitsky E.V.
The equivariant index of the C*-elliptic
operators. Izv. AN SSSR. Ser. Mat. 50 (1986), No 4, 849-865 (in
Russian),
English translation: Math. USSR Izvestija 29
(1987), No 1, 207-224.
- [3] Troitsky E.V. The index theorem for equivariant
C*-elliptic operators. Dokl. AN SSSR 282 (1985), No 5, 1059 -1061 (in
Russian), English translation: Sov. Math. Dokl. 31 (1985),
No 3, 558-560.
- [2] Troitsky E.V.
On the connection between complex and
operator topological equivariant K-theories.
Usp. Mat. Nauk. 40
(1985) No 4, 227-228 (in Russian),
English translation: Sov.
Math. Surv. 40 (1985) No 4, 243-244.
- [1] Troitsky E.V. Classifying spaces of a K-functor
associated with a C*-algebra. Vestn. Mosc. Univ. Ser. 1. Math., Mekh.
1985, No 1, 96-98 (in Russian), English translation: Moscow Univ.
Math. Bull. 40 (1985) No 1, 111-115.
