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Smirnov, Vladimir Alekseevich

Statistics Math-Net.Ru
Total publications: 40
Scientific articles: 37
Presentations: 2

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Smirnov, Vladimir Alekseevich
Professor
Doctor of physico-mathematical sciences (1986)
Speciality: 01.01.04 (Geometry and topology)
Birth date: 1.12.1949
Keywords: operads; homology and homotopy groups; spectral sequence.

Subject:

The field of scientific interests includes Operad Theory and its applications to determine the homotopy type of topological spaces, describing the Adams spectral sequence, calculation the homology groups of iterated loop spaces and the homotopy groups of spheres. The operad theory for the category of chain complexes is constructed. It is proved that the $E_\infty$-coalgebra structure on the singular chain complex of a 1-connected topological space determines the weak homotopy type of the spaces. The $E_2$- term of the Adams spectral sequence is described. The homology of iterated loop spaces over the real and complex projective spaces are calculated. The $E_\infty$- structure on the Adams spectral sequence is described. Some higher differentials of this spectral sequence are calculated.

Biography

Graduated from Faculty of Mathematics of the Moscow State Pedagogical University (MSPU) in 1967 Ph.D. thesis was defended in 1976. D.Sci. thesis was defended in 1986. A list of my works contains more than 60 titles.

   
Main publications:
  1. Smirnov V. A., “A general algebraic approach to the problem of describing the second term of the Adams spectral sequence of stable homotopy groups of spheres”, Tensor and Vector Analisis, Gordon and Breach Science Publishers, Amsterdam, 1998, 213–250  mathscinet  zmath
  2. Smirnov V. A., “Bioperady i bialgebry Khopfa v teorii kobordizmov”, Matematicheskie zametki, 65:2 (1999), 270–279  mathnet  mathscinet  zmath
  3. Smirnov V. A., “Algebra Daiera–Lashofa i algebra Stinroda dlya obobschennykh gomologii i kogomologii”, Matematicheskii sbornik, 190:12 (1999), 93–128  mathnet  mathscinet  zmath
  4. Smirnov V. A., “$A_\infty$-struktury i funktor $\mathscr D$”, Izvestiya RAN, ser. matem., 64:5 (2000), 148–162  mathnet  mathscinet  zmath
  5. Smirnov V. A., Simplicial and operad methods in algebraic topology, Transl. Math. Monogr., 198, American Mathematical Society, Providence, RI, 2001, 235 pp.  mathscinet  zmath

https://www.mathnet.ru/eng/person8539
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/227237

Publications in Math-Net.Ru Citations
2008
1. V. A. Smirnov, “Bott's Periodicity Theorem and Differentials of the Adams Spectral Sequence of Homotopy Groups of Spheres”, Mat. Zametki, 84:5 (2008),  763–771  mathnet  mathscinet  elib; Math. Notes, 84:5 (2008), 710–717  isi  scopus 1
2006
2. V. A. Smirnov, “Secondary Steenrod operations in cohomology of infinite-dimensional projective spaces”, Mat. Zametki, 79:3 (2006),  476–480  mathnet  mathscinet  zmath  elib; Math. Notes, 79:3 (2006), 440–445  isi  scopus 2
2005
3. V. A. Smirnov, “Homotopy Theories of Algebras over Operads”, Mat. Zametki, 78:2 (2005),  278–285  mathnet  mathscinet  zmath  elib; Math. Notes, 78:2 (2005), 251–257  isi  elib  scopus 2
2002
4. V. A. Smirnov, “The $A_\infty$-structures and differentials of the Adams spectral sequence”, Izv. RAN. Ser. Mat., 66:5 (2002),  193–224  mathnet  mathscinet  zmath; Izv. Math., 66:5 (2002), 1057–1086  scopus 3
2001
5. V. A. Smirnov, “A Degeneracy Criterion for $A_\infty$-Structures”, Mat. Zametki, 69:6 (2001),  906–911  mathnet  mathscinet  zmath  elib; Math. Notes, 69:6 (2001), 827–832  isi
2000
6. V. A. Smirnov, “$A_\infty$-structures and the $\mathscr D$ functor”, Izv. RAN. Ser. Mat., 64:5 (2000),  147–162  mathnet  mathscinet  zmath; Izv. Math., 64:5 (2000), 1017–1031  isi  scopus 5
1999
7. V. A. Smirnov, “$A_\infty$-simplicial objects and $A_\infty$-topological groups”, Mat. Zametki, 66:6 (1999),  913–919  mathnet  mathscinet  zmath; Math. Notes, 66:6 (1999), 754–759  isi 7
8. V. A. Smirnov, “Bioperads and Hopf bialgebras in cobordism theory”, Mat. Zametki, 65:2 (1999),  270–279  mathnet  mathscinet  zmath; Math. Notes, 65:2 (1999), 221–229  isi 2
9. V. A. Smirnov, “The Dyer–Lashof algebra and the Steenrod algebra for generalized homology and cohomology”, Mat. Sb., 190:12 (1999),  93–128  mathnet  mathscinet  zmath; Sb. Math., 190:12 (1999), 1807–1842  isi  scopus 1
1998
10. V. A. Smirnov, S. V. Kuznetsova, I. V. Mayorova, “Description of the cohomology of Banach algebras and locally convex algebras in the language of $A_\infty$-structures”, Izv. RAN. Ser. Mat., 62:4 (1998),  155–172  mathnet  mathscinet  zmath; Izv. Math., 62:4 (1998), 789–805  isi  scopus 1
11. V. A. Smirnov, “Lie algebras over operads and their applications in homotopy theory”, Izv. RAN. Ser. Mat., 62:3 (1998),  121–154  mathnet  mathscinet  zmath; Izv. Math., 62:3 (1998), 549–580  isi  scopus 12
12. V. A. Smirnov, “The $E_2$ term of the spectral sequence of unstable homotopy groups of topological spaces”, Mat. Zametki, 64:5 (1998),  792–796  mathnet  mathscinet  zmath; Math. Notes, 64:5 (1998), 684–688  isi
13. V. A. Smirnov, “Homotopy type and $A_\infty$-group structure”, Mat. Sb., 189:10 (1998),  135–144  mathnet  mathscinet  zmath; Sb. Math., 189:10 (1998), 1563–1572  isi  scopus 1
1997
14. V. A. Smirnov, “Description of the homology of groups and algebras”, Izv. RAN. Ser. Mat., 61:3 (1997),  203–212  mathnet  mathscinet  zmath; Izv. Math., 61:3 (1997), 663–671  isi  scopus
15. V. A. Smirnov, “Calculation of the $E_\infty$-structure on the Milnor coalgebra”, Mat. Zametki, 62:3 (1997),  479–480  mathnet  mathscinet  zmath; Math. Notes, 62:3 (1997), 399–401  isi
16. V. A. Smirnov, “$E_\infty$-structures on homotopy groups”, Mat. Zametki, 61:1 (1997),  152–156  mathnet  mathscinet  zmath; Math. Notes, 61:1 (1997), 127–130  isi 2
1996
17. V. A. Smirnov, “Description of stable homotopy groups of spheres in the language of $A_\infty$-algebras”, Uspekhi Mat. Nauk, 51:1(307) (1996),  171–172  mathnet  mathscinet  zmath; Russian Math. Surveys, 51:1 (1996), 171–172  isi  scopus
1994
18. V. A. Smirnov, “Homology of $B$-constructions and co-$B$-constructions”, Izv. RAN. Ser. Mat., 58:4 (1994),  80–96  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 45:1 (1995), 79–95  isi 15
1993
19. V. A. Smirnov, “Homology of $\mathscr{A}_\infty$-algebras”, Dokl. Akad. Nauk, 330:4 (1993),  441–443  mathnet  mathscinet  zmath; Dokl. Math., 47:3 (1993), 534–537 1
1992
20. V. A. Smirnov, “Secondary operations in the homology of the operad $E$”, Izv. RAN. Ser. Mat., 56:2 (1992),  449–468  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 40:2 (1993), 425–442  isi 11
21. V. A. Smirnov, “Cohomology of the Steenrod algebra”, Mat. Zametki, 52:2 (1992),  120–126  mathnet  mathscinet  zmath; Math. Notes, 52:2 (1992), 893–844 1
1991
22. V. A. Smirnov, V. A. Sheikhman, “Continuation of homogeneous functionals with a given convexity”, Mat. Zametki, 50:5 (1991),  90–96  mathnet  mathscinet  zmath; Math. Notes, 50:5 (1991), 1157–1161  isi 1
23. V. A. Smirnov, “Homology of symmetric products”, Mat. Zametki, 49:1 (1991),  104–113  mathnet  mathscinet  zmath; Math. Notes, 49:1 (1991), 73–80  isi
1990
24. V. A. Smirnov, Chan Khuen, “On the funktor Ext in the category of linear topological spases”, Izv. Akad. Nauk SSSR Ser. Mat., 54:1 (1990),  188–200  mathnet  mathscinet  zmath; Math. USSR-Izv., 36:1 (1991), 199–210 2
1989
25. V. A. Smirnov, “On the chain complex of an iterated loop space”, Izv. Akad. Nauk SSSR Ser. Mat., 53:5 (1989),  1108–1119  mathnet  mathscinet  zmath; Math. USSR-Izv., 35:2 (1990), 445–455 3
26. V. A. Smirnov, “Functional homology operations and the weak homotopy type”, Mat. Zametki, 45:5 (1989),  76–86  mathnet  mathscinet  zmath; Math. Notes, 45:5 (1989), 400–406  isi 5
1987
27. V. A. Smirnov, “Hopf radical algebras and the Steenrod algebra”, Uspekhi Mat. Nauk, 42:2(254) (1987),  245–246  mathnet  mathscinet  zmath; Russian Math. Surveys, 42:2 (1987), 301–302  isi 1
1986
28. V. A. Smirnov, “Secondary cohomology operations”, Dokl. Akad. Nauk SSSR, 288:2 (1986),  301–304  mathnet  mathscinet  zmath 1
1985
29. V. A. Smirnov, “Homotopy theory of coalgebras”, Izv. Akad. Nauk SSSR Ser. Mat., 49:6 (1985),  1302–1321  mathnet  mathscinet  zmath; Math. USSR-Izv., 27:3 (1986), 575–592 27
1981
30. V. A. Smirnov, “On the cochain complex of topological spaces”, Mat. Sb. (N.S.), 115(157):1(5) (1981),  146–158  mathnet  mathscinet  zmath; Math. USSR-Sb., 43:1 (1982), 133–144 26
1980
31. V. A. Smirnov, “Homology of fibre spaces”, Uspekhi Mat. Nauk, 35:3(213) (1980),  227–230  mathnet  mathscinet  zmath; Russian Math. Surveys, 35:3 (1980), 294–298  isi 16
1978
32. V. A. Smirnov, “Twisted Cartesian products”, Mat. Zametki, 24:5 (1978),  723–732  mathnet  mathscinet  zmath; Math. Notes, 24:5 (1978), 886–890
1977
33. V. A. Smirnov, “Functor $D$ and strong homotopy”, Mat. Zametki, 21:4 (1977),  557–564  mathnet  mathscinet  zmath; Math. Notes, 21:4 (1977), 311–315 2
1976
34. V. A. Smirnov, “$D$ Functor for tensor cross products”, Mat. Zametki, 20:4 (1976),  465–472  mathnet  mathscinet  zmath; Math. Notes, 20:4 (1976), 819–823 8
1975
35. V. A. Smirnov, “Homology of twisted tensor products”, Dokl. Akad. Nauk SSSR, 222:5 (1975),  1041–1044  mathnet  mathscinet  zmath 3
36. V. A. Smirnov, “Twisted tensor products and strong homotopy”, Dokl. Akad. Nauk SSSR, 222:2 (1975),  288–290  mathnet  mathscinet  zmath
1974
37. V. A. Smirnov, “Twisted tensor products and Hirsch's theory”, Dokl. Akad. Nauk SSSR, 219:2 (1974),  294–296  mathnet  mathscinet  zmath

2015
38. I. Smirnova, V. Smirnov, “Каскады из правильных многогранников”, Kvant, 2015, no. 3,  32–33  mathnet
2006
39. I. Smirnova, V. Smirnov, “Вписанные и описанные многоугольники”, Kvant, 2006, no. 4,  31  mathnet
1998
40. D. V. Anosov, P. M. Akhmet'ev, A. A. Bolibrukh, V. M. Buchstaber, V. A. Kolosov, A. A. Mal'tsev, S. P. Novikov, V. A. Smirnov, A. V. Chernavskii, “Mikhail Mikhailovich Postnikov (on his 70th birthday)”, Uspekhi Mat. Nauk, 53:2(320) (1998),  183–184  mathnet  mathscinet  zmath; Russian Math. Surveys, 53:2 (1998), 431–433  isi

Presentations in Math-Net.Ru
1. О некоторых свойствах параболы, эллипса и гиперболы
V. A. Smirnov
Differential geometry and applications
May 6, 2024 16:45
2. Об оценке центральной симметричности фигур и двух новых замечательных точках треугольника
V. A. Smirnov
Differential geometry and applications
February 20, 2016 16:45

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