O.Viro's publications





66. Pictorial calculus for isometries, American Mathematical Monthly, Vol. 123, No. 1, January 2016, 82-87. Copyright 2016 Mathematical Association of America. All Rights Reserved.

65. Space of smooth 1-knots in a 4-manifold: is its algebraic topology sensitive to smooth structures? Arnold Mathematical Journal (2015) 1:1, 83-86.

64. Biflippers and head to tail composition rules, arXiv:1412.2397 [math.MG]   

63. Defining relations for reflections, arXiv:1405.1460 [math.MG].   

62. 1-manifolds, Bulletin of the Manifold Atlas (2013), Accepted:28th May 2013 http://www.boma.mpim-bonn.mpg.de/.

61. On basic concepts of tropical geometry (Russian) Trudy MIAN, 2011, vol. 273, 271-303. ; English translation in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2011, Vol. 273, pp. 271-303.

60. Hyperfields for Tropical Geometry I. Hyperfields and dequantization, arXiv:1006.3034

59. Elementary Topology (joint with O.A.Ivanov, N.Yu.Netsvetaev, V.M.Kharlamov) Moscow Center for Continuous Mathematical Education, 2010, 352 pages. ISBN 978-5-94057-587-0 (Russian).

58. Twisted acyclicity of a circle and signatures of a link, Journal of Knot Theory and Its Ramifications, 18:6 (2009), 729-755.   

57. Elementary Topology Problem Textbook. (joint with O.A.Ivanov, N.Yu.Netsvetaev, V.M.Kharlamov) American Mathematical Society, 2008, 400 pages. ISBN 978-0-8218-4506-6.

56. From the sixteenth Hilbert problem to Tropical Geometry, Japan. J. Math, vol. 3 (2008), pp. 1-30 .

55. Asymptotically Maximal Real Algebraic Hypersurfaces of Projective Space,   (joint with Ilia Itenberg) Proceedings of 13th Gokova Geometry-Topology Conference, International Press, 2007 .

54. Virtual Links, Orientations of Chord Diagrams and Khovanov Homology,   Proceedings of 12th Gokova Geometry-Topology Conference, International Press, 2006, pp. 184 - 209. ]; see also arXiv: math.GT/0611406 [abs, .

53. Whitney Number of Closed Real Algebraic Affine Curve of Type I,   (2006) arXiv:math.AG/0602256 abs, ps, , Moscow Math.J. 6:1 (2006).

52. Khovanov homology, its definitions and ramifications, Fund. Math. 184 (2004), 317-342.

51. Quantum Relatives of Alexander Polynomial,   (2002) arXiv:math.GT/0204290 abs, ps, , Russian version: ;
Algebra i Analiz 18:3 (2006) 63-157 (in Russian) , with English translation to be published in St.Petersburg Math. J.

50. Remarks on definition of Khovanov homology,   (2002) arXiv:math.GT/0202199 abs, ps, .

49. What is an amoeba,   Notices AMS, 49:8 (2002), 916-917, ps, .

48. Congruence modulo 8 for real algebraic curves of degree 9,  
joint with  S. Yu. Orevkov   Russ. Math. Surv., 2001, 56 (4), 770-771;
PDF file of Russian original PDF file of expanded English translation.

47. Dequantization of Real Algebraic Geometry on a Logarithmic Paper, Proceedings of the 3rd European Congress of Mathematicians, Birkhäuser, Progress in Math, 201, (2001), 135--146. ;
arXiv:math.AG/0005163 abs, ps,

46. Encomplexing the writhe, "Topology, Ergodic Theory, Real Algebraic Geometry. Rokhlin's Memorial" Amer. Math.Soc. Transl. ser 2, vol 202, ed. V. Turaev and A. Vershik; arXiv:math.GT/0005162 abs, ps, .
A preliminary version of the same preprint:
Self-Linking Number of  Real Algebraic Link, (1999) abs, ps, .

45. On the Casson knot invariant, (joint with Michael Polyak), J. Knot Theory and Its Ramifications;  10 (2001), no. 5, 711--738.
arXiv:math.GT/9903158 [abs, ps, ].

44. Finite type invariants of classical and virtual knots, (joint with M.N.Goussarov and M.Polyak), Topology;  39, no. 5, (2000) pp.1045-1068.
arXiv:math.GT/9810073[abs, ps, ].

43. Mutual position of hypersurfaces in projective space, Amer. Math. Soc. Transl. (2) Vol. 186  ;  (1998), 161-176; [abs, ].

42. Patchworking algebraic curves disproves the Ragsdale conjecture, (joint with Ilia Itenberg), The Mathematical Intelligencer   18:1  (1996), 19-28; [abspdf part 1, pdf part 2]
Preprint Uppsala University U.U.D.M. Report 1995:8.

41. Generic immersions of circle to surfaces and complex topology of real algebraic curves, Topology of real algebraic varieties and related topics, (a volume dedicated to memory of D.A.Gudkov ), AMS Translations,  Series 2, 173, (1995) 231-252; [abs,   ].

40. Gauss diagram formulas for Vassiliev invariants, (joint with Michael Polyak) International Mathematics Research Notes 1994:11. [ pdf]

39. Complex orientations of real algebraic surfaces, Topology of manifolds and varieties, Advances of Soviet Math. 18 (1994), 261-284; [abs, ]; see also arXive: math.AG/0611396 [abs, ].

38. An inequality for the number of nonempty ovals of a curve of odd degree (joint with V.I.Zvonilov), Algebra i analiz 4:3 (1992) 159-170 (Russian) [];
English translation in St. Petersburg Math. J. 4:3 (1993) [].

37. Moves of triangulations of a PL-manifold, Quantum groups (Leningrad, 1990), 367--372, Lecture Notes in Math., 1510, Springer, Berlin, 1992.)

36.  Lectures on combinatorial presentations of manifolds, In book Differential geometry and topology (Alghero, 1992) World Sci. Publ., River Edge, NJ (1993) 244-264.

35. State sum invariants of 3-manifolds and quantum 6j-symbols (joint with V.G.Turaev), Topology 31:4 (1992) 865-902; [].

34. Plane real algebraic curves: constructions with controlled topology Algebra i analiz 1:5 (1989) 1-73 (Russian) [];
English translation in Leningrad Math. J. 1:5 (1990) 1059-1134; [].

33. Compact four-dimensional exotica with small homology, Algebra i analiz 1:4 (1989) 67-77 (Russian) [];
English translation in Leningrad Math. J. 1:4 (1990) 871-880. [abs,  ps].

32. Configurations of skew lines (joint with Ju.V.Drobotukhina), Algebra i analiz 1:4 (1989) 222-246 (Russian)
English translation in Leningrad Math. J. 1:4 (1990) 1027-1050 [ ].
Revision of 2000 [abs, ps, ]. Revision of 2006 [] View.

31. Interlacing of skew lines (joint with Ju.V.Drobotukhina), Kvant (1988) No. 3, 12-19 (Russian).

30. Problems in Topology (joint with O.A.Ivanov, N.Yu.Netsvetaev and V.M.Kharlamov), Leningrad, LGU, 1988 (Russian); Second, extended edition: St.Petersburg, SPbU, 2000.))

29. Homology and cohomology (joint with D.B.Fuchs), Current problems in mathematics. Fundamental directions, Vol. 24, 123--240, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1988 (Russian). English translation by C.J.Shaddock, Encyclopaedia Math. Sci., 24, Topology. II, 95--196, Springer, Berlin, 2004.

28. Introduction to homotopy theory (joint with D.B.Fuchs), Current problems in mathematics. Fundamental directions, f Vol. 24, 6--121, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1988 (Russian). English translation by C. J. Shaddock, Encyclopaedia Math. Sci., 24, Topology. II, 1--93, Springer, Berlin, 2004.

27. Extensions of the Gudkov-Rohlin congruence (joint with V.M.Kharlamov), Lecture Notes in Math. 1346 (1988) 357-406, Springer-Verlag, Heidelberg and New-York [pdf part 1], [pdf part 2].

26. Some integral calculus based on Euler characteristic, Lecture Notes in Math. 1346 (1988) 127-138, Springer-Verlag, Heidelberg and New-York [].

25. Non-diffeomorphic but homeomorphic knottings of surfaces in the 4-sphere (joint with S.M.Finashin and M.Kreck), Lecture Notes in Math. 1346 (1988) 157-198, Springer-Verlag, Heidelberg and New-York [].

24. Exotic knottings of surfaces in the 4-sphere (joint with S.M.Finashin and M.Kreck), Bull. Amer. Math. Soc. 17:2 (1987) 287-290.

23. Progress of the last six years in topology of real algebraic varieties, Uspekhi Mat. Nauk 41:3 (1986) 45-67 (Russian) []
English translation in Russian Math. Surveys 41:3 (1986) 55-82 [].

22. Topological problems on lines and points of the three-dimensional space, Doklady AN SSSR 284:5 (1985) 1049-1052 (Russian);
English translation in Soviet Math. Doklady 32:2 (1985) 528-531 [].

21. The signature of a branched covering, Mat. zametki 36:4 (1984) 549-557 (Russian)[]; English translation in Math. Notes 36:3-4 772-776.

20. Gluing of plane real algebraic curves and constructions of curves of degrees 6 and 7, Lecture Notes in Math. 1060 (1984) 187-200, Springer-Verlag, Berlin and New York [].

19. Intersections of loops on two-dimensional manifolds. II. Free loops (joint with V.G.Turaev), Mat. sbornik 121:3 (1983) 359-369 (Russian)[]; English translation in Soviet Math. Sbornik.

18. Progress over the last 5 years in topology of real algebraic varieties, Proceedings of the International Congress of Mathematicians, Aug. 16-24, 1983 vol. 1, Warszawa PWN, Warsaw 595-611 (Russian).

17. Plane real algebraic curves of degrees 7 and 8: new restrictions, Izvestiya AN SSSR, ser. Matem. 47:5 (1983) 1135-1150 (Russian)[];
English transl. in Soviet Math. Izvestia.

16. Gluing algebraic hypersurfaces and constructions of curves, Tezisy Leningradskoj Mezhdunarodnoj Topologicheskoj Konferencii 1982, Nauka (1983) 149-197 (Russian). English translation of the main chapter is in the preprint Patchworking Real Algebraic Varieties, arXiv:math/0611382 [math.AG] [].

15. Complex orientations of real algebraic surfaces, Uspekhi Mat. Nauk 37:4 (1982) 93 (Russian).

14. Colored knots, Kvant (1981) No. 3, 8-14 (Russian) [gif]; English translation: Tied into Knot Theory: unraveling the basics of mathematical knots. Quantum 8 (1998), no. 5, 16-20.

13. Curves of degree 7, curves of degree 8 and Ragsdale conjecture, Doklady AN SSSR 254:6 (1980) 1305-1310 (Russian);
English transl. in Soviet Math. Doklady 22 (1980), No. 2, 566-570 [].

12. Constructing multicomponent real algebraic surfaces, Doklady AN SSSR 248:2 (1979) 279-282 (Russian);
English transl. in Soviet Math. Doklady 20 (1979), No. 3, 991-995 [].

11. Constructing M-surfaces, Funkts. analiz i ego prilozh. 13:3 (1979) 71-72 (Russian)[];
English transl. in Functional Anal. Appl. 13:3 (1979), 212-213 [].

10. Generalizing Petrovsky and Arnold inequalities for curves with singularities, Uspekhi Mat. Nauk 33:3 (1978) 145-146 (Russian).

9. Estimates for twisted homology, (joint with V.G.Touraev), Tezisy VII Vsesoyuznoj topologicheskoj konferencii (1977) 42 (Russian).

8. Signatures of links, Tezisy VII Vsesoyuznoj topologicheskoj konferencii (1977) 41 (Russian), English verison.

7. The Volodin-Kuznetsov-Fomenko conjecture on Heegaard diagrams of 3-dimensional sphere is not true, (joint with V.L.Kobelsky), Uspekhi Mat. Nauk   32:5 (1977) 175-176 (Russian).[]

6. Placements in codimension 2 and boundary, Uspekhi Mat. Nauk 30:1 (1975) 231-232 (Russian).[]

5. Non-projecting isotopies and knots with homeomorphic covering spaces, Zap. Nauchn. Semin. LOMI  66 (1976) 133-147 (Russian) [];
English transl. in J. Soviet Math.   12:1(1979) 86-96.

4. Branched coverings of manifolds with boundary and invariants of links. I, Izvestiya AN SSSR, ser. Matem.   37:6 (1973) 1242-1259 (Russian) [];
English translation in Soviet Math. Izvestia.

3. Two-fold branched coverings of three-dimensional sphere, Zap. Nauchn. Semin. LOMI   36 (1973) 6-39 (Russian) [];
English transl. in J. Soviet Math  8:5 (1977) 531-553.

2. Local knotting of submanifolds, Matem. sbornik  90:2 (1973) 172-181 (Russian) [];
English translation in Soviet Math. Sbornik.

1. Links, two-fold branched coverings and braids, Matem. sbornik   87:2 (1972) 216-228 (Russian) [];
English translation in Soviet Math. Sbornik.


2015-12-16