RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 
Sklyarenko, Evgenii Grigor'evich
(1935–2009)

Statistics Math-Net.Ru
Total publications: 54
Scientific articles: 50

Number of views:
This page:1209
Abstract pages:13009
Full texts:5898
References:863
Professor
Doctor of physico-mathematical sciences (1964)
Speciality: 01.01.04 (Geometry and topology)
Birth date: 3.08.1935
Keywords: compactification theory; homological dimension; locally compact groups and coset spaces; sheaves in homology and cohomology theory; homological methods in topological problems; spectral sequences; hyperhomology; general forms of Poincare duality; homological and cohomological multiplications; limit passages and inverse limit derived functors; relative homological algebra; de Rahm cohomology with locally constant coefficients.

Subject:

Modern methods of homology and cohomology theory applications to various problems in general topology are presented. These methods are based on the wide usage of the sheaf theory apparatus and adequate means of homological algebra. Among examined problems there are various homological characteristics of the dimension, the behaviour of the dimension, under various continuous mappings, homological type conditions for spreads of homeomorphisms and some mappings on suitable compactifications of topological spaces, special sort compactifications, homological locally connected spaces and generalized manifolds, general forms and categorical nature of Poincare duality, a common construction of (co)homological product operations, common categorical nature of suitable filtrations in homology of topological spaces, homological structures of mappings and adequate spectral sequences, limit passages in homology theory, axiom problems for (co)homology groups and homological products. Homological algebra constructions reflecting the general categorical nature of various relations of homological type in topology are also presented.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1958 (department of higher geometry and topology). Ph.D. thesis was defended in 1961. D.Sci. thesis was defended in 1964. A list of my works contains more than 60 titles. Since 1985 I have led the research seminar at MSU on homology theory. There are 16 Ph.D. and 2 D.Sci. among my pupils.

   
Main publications:
  • Sklyarenko E. G. K teorii obobschennykh mnogoobrazii // Izvestiya AN SSSR, ser. matem., 1971, 35(4), 831–843.
  • Sklyarenko E. G. Otnositelnaya gomologicheskaya algebra v kategorii modulei // Uspekhi matem. nauk, 1978, 33(3), 85–120.
  • Sklyarenko E. G. Gomologii i kogomologii obschikh prostranstv // VINITI, Itogi nauki i tekhniki, sovremennye problemy matematiki, fundamentalnye napravleniya, 1989, 50, 129–266.
  • Sklyarenko E. G. O prirode gomologicheskikh umnozhenii dvoistvennosti // Uspekhi matem. nauk, 1994, 49(1), 141–198.
  • Sklyarenko E. G. Giper(ko)gomologii dlya tochnykh sleva kovariantnykh funktorov i teoriya gomologii topologicheskikh prostranstv // Uspekhi matem. nauk, 1995, 50(3), 109–146.

http://www.mathnet.ru/eng/person8501
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/223507

Publications in Math-Net.Ru
2008
1. E. G. Sklyarenko, “Two Orientations”, Mat. Zametki, 83:1 (2008),  95–106  mathnet  mathscinet  zmath  elib; Math. Notes, 83:1 (2008), 88–96  isi  elib  scopus
2. E. G. Sklyarenko, “The homological degree and Hopf's absolute degree”, Mat. Sb., 199:11 (2008),  113–140  mathnet  mathscinet  zmath  elib; Sb. Math., 199:11 (2008), 1687–1713  isi  elib  scopus
2005
3. E. G. Sklyarenko, “A topological version of the argument principle and Rouche's theorem”, Fundam. Prikl. Mat., 11:5 (2005),  209–223  mathnet  mathscinet  zmath  elib; J. Math. Sci., 146:1 (2007), 5592–5602  scopus
4. E. G. Sklyarenko, “On locally free Abelian groups”, Mat. Zametki, 77:1 (2005),  121–126  mathnet  mathscinet  zmath  elib; Math. Notes, 77:1 (2005), 112–116  isi  scopus
2004
5. E. G. Sklyarenko, “Dual Homology for the de Rham Cohomology”, Tr. Mat. Inst. Steklova, 247 (2004),  237–246  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 247 (2004), 217–226
2003
6. E. G. Sklyarenko, “The Thom isomorphism for nonorientable bundles”, Fundam. Prikl. Mat., 9:4 (2003),  55–103  mathnet  mathscinet  zmath  elib; J. Math. Sci., 136:5 (2006), 4166–4200  elib  scopus
1999
7. E. G. Sklyarenko, “Flabby sheaves of chains for singular cohomology”, Mat. Zametki, 65:3 (1999),  396–401  mathnet  mathscinet  zmath; Math. Notes, 65:3 (1999), 331–334  isi
1997
8. E. G. Sklyarenko, “On homological products”, Izv. RAN. Ser. Mat., 61:1 (1997),  157–176  mathnet  mathscinet  zmath; Izv. Math., 61:1 (1997), 161–181  isi  scopus
9. E. G. Sklyarenko, “Filtrations in hyperhomology”, Mat. Zametki, 61:4 (1997),  578–582  mathnet  mathscinet  zmath; Math. Notes, 61:4 (1997), 480–483  isi
10. E. G. Sklyarenko, “On enclosure homology”, Mat. Sb., 188:2 (1997),  129–136  mathnet  mathscinet  zmath; Sb. Math., 188:2 (1997), 299–306  isi  scopus
1996
11. E. G. Sklyarenko, “On cohomologies with supports”, Uspekhi Mat. Nauk, 51:1(307) (1996),  167–168  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:1 (1996), 167–168  isi  scopus
1995
12. E. G. Sklyarenko, “Hyper(co)homology for exact left covariant functors and a homology theory for topological spaces”, Uspekhi Mat. Nauk, 50:3(303) (1995),  109–146  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:3 (1995), 575–611  isi
1994
13. E. G. Sklyarenko, “On the nature of homological products and duality”, Uspekhi Mat. Nauk, 49:1(295) (1994),  141–198  mathnet  mathscinet  zmath; Russian Math. Surveys, 49:1 (1994), 151–215  isi
1992
14. E. G. Sklyarenko, “Connection homology and cohomology between sets. Enclosure homology and cohomology of a closed set”, Izv. RAN. Ser. Mat., 56:5 (1992),  1040–1071  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 41:2 (1993), 307–335  isi
15. E. G. Sklyarenko, “On Zeeman's filtration in homology”, Mat. Sb., 183:12 (1992),  103–116  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 77:2 (1994), 477–488  isi
16. E. G. Sklyarenko, “Homology and cohomology. Limit passages”, Trudy Mat. Inst. Steklov., 193 (1992),  162–168  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 193 (1993), 179–185
1991
17. E. G. Sklyarenko, “Many-dimensional version of Cauchy's theorem on residues”, Mat. Zametki, 49:3 (1991),  109–113  mathnet  mathscinet  zmath; Math. Notes, 49:3 (1991), 302–304  isi
1989
18. E. G. Sklyarenko, “General homology and cohomology theory. The current state and typical applications”, Itogi Nauki i Tekhniki. Ser. Algebra. Topol. Geom., 27 (1989),  125–228  mathnet  mathscinet  zmath; J. Soviet Math., 57:2 (1991), 3009–3066
19. E. G. Sklyarenko, “The homology and cohomology of general spaces”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 50 (1989),  129–266  mathnet  mathscinet  zmath
1984
20. E. G. Sklyarenko, “Some applications of the functor $\varprojlim^1$”, Mat. Sb. (N.S.), 123(165):3 (1984),  369–390  mathnet  mathscinet  zmath; Math. USSR-Sb., 51:2 (1985), 367–387
1980
21. E. G. Sklyarenko, “On homologically locally connected spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 44:6 (1980),  1417–1433  mathnet  mathscinet  zmath; Math. USSR-Izv., 17:3 (1981), 601–614  isi
22. E. G. Sklyarenko, “Poincaré duality and relations between the functors Ext and Tor”, Mat. Zametki, 28:5 (1980),  769–776  mathnet  mathscinet  zmath; Math. Notes, 28:6 (1980), 841–845  isi
1979
23. E. G. Sklyarenko, “On homology theory associated with the Aleksandrov–Čech cohomology”, Uspekhi Mat. Nauk, 34:6(210) (1979),  90–118  mathnet  mathscinet  zmath; Russian Math. Surveys, 34:6 (1979), 103–137
1978
24. E. G. Sklyarenko, “Relative homological algebra in categories of modules”, Uspekhi Mat. Nauk, 33:3(201) (1978),  85–120  mathnet  mathscinet  zmath; Russian Math. Surveys, 33:3 (1978), 97–137
25. E. G. Sklyarenko, “Pure and finitely presentable modules, duality homomorphisms and the coherence property of a ring”, Mat. Sb. (N.S.), 105(147):2 (1978),  192–206  mathnet  mathscinet  zmath; Math. USSR-Sb., 34:2 (1978), 173–186
1971
26. E. G. Sklyarenko, “On the theory of generalized manifolds”, Izv. Akad. Nauk SSSR Ser. Mat., 35:4 (1971),  831–843  mathnet  mathscinet  zmath; Math. USSR-Izv., 5:4 (1971), 845–857
27. E. G. Sklyarenko, “Uniqueness theorems in homology theory”, Mat. Sb. (N.S.), 85(127):2(6) (1971),  201–223  mathnet  mathscinet  zmath; Math. USSR-Sb., 14:2 (1971), 199–218
1969
28. E. G. Sklyarenko, “Uniform edging structures”, Dokl. Akad. Nauk SSSR, 186:1 (1969),  39–42  mathnet  mathscinet  zmath
29. E. G. Sklyarenko, “Homology theory and the exactness axiom”, Uspekhi Mat. Nauk, 24:5(149) (1969),  87–140  mathnet  mathscinet  zmath; Russian Math. Surveys, 24:5 (1969), 91–142
1968
30. E. G. Sklyarenko, “Almost acyclic mappings”, Mat. Sb. (N.S.), 75(117):2 (1968),  296–302  mathnet  mathscinet  zmath; Math. USSR-Sb., 4:2 (1968), 267–272
1967
31. E. M. Beniaminov, E. G. Sklyarenko, “Local cohomology groups”, Dokl. Akad. Nauk SSSR, 176:5 (1967),  987–990  mathnet  mathscinet  zmath
1966
32. E. G. Sklyarenko, “On linked cycles”, Uspekhi Mat. Nauk, 21:4(130) (1966),  77–90  mathnet  mathscinet  zmath; Russian Math. Surveys, 21:4 (1966), 63–75
33. E. G. Sklyarenko, “Certain remarks on limit spaces of Postnikov systems”, Mat. Sb. (N.S.), 69(111):1 (1966),  61–64  mathnet  mathscinet  zmath
1965
34. E. G. Sklyarenko, “On the definition of cohomology dimension”, Dokl. Akad. Nauk SSSR, 161:3 (1965),  538–539  mathnet  mathscinet  zmath
1964
35. E. G. Sklyarenko, “Some applications of the theory of sheaves in general topology”, Uspekhi Mat. Nauk, 19:6(120) (1964),  47–70  mathnet  mathscinet  zmath; Russian Math. Surveys, 19:6 (1964), 41–62
1963
36. E. G. Sklyarenko, “On a theorem of Vietoris and Begle”, Dokl. Akad. Nauk SSSR, 149:2 (1963),  264–267  mathnet  mathscinet  zmath
37. E. G. Sklyarenko, “Bicompactifications with punctiform boundary and their cohomology groups”, Izv. Akad. Nauk SSSR Ser. Mat., 27:5 (1963),  1165–1180  mathnet  mathscinet  zmath
38. E. G. Sklyarenko, “Some applications of the theory of sheaves in general topology”, Uspekhi Mat. Nauk, 18:2(110) (1963),  187–188  mathnet
39. E. G. Sklyarenko, “On the topological structure of locally bicompact groups and their factor spaces”, Mat. Sb. (N.S.), 60(102):1 (1963),  63–88  mathnet  mathscinet  zmath
1962
40. E. G. Sklyarenko, “On perfect bicompact extensions”, Dokl. Akad. Nauk SSSR, 146:5 (1962),  1031–1034  mathnet  mathscinet  zmath
41. E. G. Sklyarenko, “On the topological structure of factor spaces of locally bicompact groups”, Dokl. Akad. Nauk SSSR, 145:5 (1962),  1004–1007  mathnet  mathscinet  zmath
42. E. G. Sklyarenko, “Two theorems on infinite-dimensional spaces”, Dokl. Akad. Nauk SSSR, 143:5 (1962),  1053–1056  mathnet  mathscinet  zmath
43. E. G. Sklyarenko, “Some questions in the theory of bicompactifications”, Izv. Akad. Nauk SSSR Ser. Mat., 26:3 (1962),  427–452  mathnet  mathscinet  zmath
1961
44. E. G. Sklyarenko, “On the extension of homeomorphisms”, Dokl. Akad. Nauk SSSR, 141:5 (1961),  1045–1047  mathnet  mathscinet  zmath
45. E. G. Sklyarenko, “Infinite-dimensional homogeneous spaces”, Dokl. Akad. Nauk SSSR, 141:4 (1961),  811–813  mathnet  mathscinet  zmath
46. E. G. Sklyarenko, “Perfect bicompact extensions”, Dokl. Akad. Nauk SSSR, 137:1 (1961),  39–41  mathnet  mathscinet  zmath
1960
47. E. G. Sklyarenko, “Representation of infinite-dimensional compacta as an inverse limit of polyhedra”, Dokl. Akad. Nauk SSSR, 134:4 (1960),  773–775  mathnet  mathscinet  zmath
1959
48. E. G. Sklyarenko, “Dimensionality properties of infinite-dimensional spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 23:2 (1959),  197–212  mathnet  mathscinet  zmath
1958
49. E. Sklyarenko, “On the imbedding of normal spaces into bicompacts of the same weight and dimension”, Dokl. Akad. Nauk SSSR, 123:1 (1958),  36–39  mathnet  mathscinet  zmath
50. E. Sklyarenko, “Bicompact extensions of semibicompact spaces”, Dokl. Akad. Nauk SSSR, 120:6 (1958),  1200–1203  mathnet  mathscinet  zmath

2002
51. V. M. Buchstaber, A. V. Zarelua, A. A. Mal'tsev, E. F. Mishchenko, E. A. Morozova, S. P. Novikov, V. I. Ponomarev, M. M. Postnikov, E. G. Sklyarenko, V. V. Fedorchuk, “Yurii Mikhailovich Smirnov (on his 80th birthday)”, Uspekhi Mat. Nauk, 57:2(344) (2002),  203–207  mathnet  mathscinet  zmath; Russian Math. Surveys, 57:2 (2002), 431–436  isi
1981
52. E. G. Sklyarenko, “Yu. G. Borisovich, N. M. Bliznyakov, Ya. A. Izrailevich, T. N. Fomenko, Introduction to Topology (a review)”, Uspekhi Mat. Nauk, 36:2(218) (1981),  241–245  mathnet
53. E. G. Sklyarenko, “R. A. Aleksandryan and È. A. Mirzakhanyan, General Topology (a review)”, Uspekhi Mat. Nauk, 36:2(218) (1981),  239–240  mathnet
1975
54. P. S. Aleksandrov, N. V. Efimov, E. G. Sklyarenko, “In memory of Lev Abramovich Tumarkin”, Uspekhi Mat. Nauk, 30:3(183) (1975),  151–153  mathnet  mathscinet  zmath; Russian Math. Surveys, 30:3 (1975), 135–137

Organisations
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020