## O.Viro's publications |

**70.***
Rokhlin's signature theorems,* joint with Sergey Finashin
and Viatcheslav Kharlamov, arXiv:2012.02004 [math.HO]

**69.***
Fundamental group in the projective knot theory,* joint with
Julia Viro, arXiv:2006.04032 [math.GT], ; to be published in the book: Topology and
geometry: a collection of essays dedicated to Vladimir G. Turaev, European
Mathematical Society Press, Berlin, 2021.

**68.***
Choreography of divisors on algebraic curves ,*
arXiv:1909.05556 [math.AG]

**67.***
Characterization of affine links in the projective space,*
arXiv:1901.07686 [math.GT]

**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, .

**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,
*
.

**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; [
].

**42.** *Patchworking algebraic curves disproves the Ragsdale
conjecture, *(joint with Ilia Itenberg), The Mathematical Intelligencer
**18:1 **(1996), 19-28; [abs,
pdf 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,
pdf].

**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 1999 [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) [];
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.

2019-08-25