J. W. Alexander, A Lemma on Systems of Knotted Curves, Proc. Nat
DOI : 10.1073/pnas.9.3.93

V. I. Arnold, The Vassilierv theory of Discriminants and knots. First european congress of mathematics, pp.3-29

E. Artin, Theorie der Zpfe, Abh. Math. Sem. Univ. Hamburg, vol.4, pp.27-72, 1925.

D. Bar-natan, On the Vassiliev knot invariants, Topology, pp.423-472, 1995.

V. G. Bardakov, Virtual and welded links and their invariants, Elektron. Mat. Izv, vol.2, issue.electronic, p.196199, 2005.

V. G. Bardakov, The virtual and universal braids, Fundamenta Mathematicae, vol.184, p.118, 2004.
DOI : 10.4064/fm184-0-1

V. G. Bardakov and P. Bellingeri, Combinatorial properties of virtual braids, Topology and its Applications, vol.156, issue.6, pp.1071-1082, 2009.
DOI : 10.1016/j.topol.2008.10.002
URL : https://hal.archives-ouvertes.fr/hal-00096888

V. G. Bardakov, A. Y. Vesnin, and B. Wiest, DYNNIKOV COORDINATES ON VIRTUAL BRAID GROUPS, Journal of Knot Theory and Its Ramifications, vol.21, issue.05, pp.1250052-1250062, 2012.
DOI : 10.1142/S021821651101005X
URL : https://hal.archives-ouvertes.fr/hal-00577935

L. Bartholdi, B. Enriquez, P. Etingof, and E. Rains, Groups and Lie algebras corresponding to the Yang???Baxter equations, Journal of Algebra, vol.305, issue.2, p.742764, 2006.
DOI : 10.1016/j.jalgebra.2005.12.006
URL : https://hal.archives-ouvertes.fr/hal-00203469

J. Birman, New points of view in knot theory, Bulletin of the American Mathematical Society, vol.28, issue.2, p.253287, 1993.
DOI : 10.1090/S0273-0979-1993-00389-6

J. S. Birman and N. J. , Braids, links, and mapping class groups, Annals of Mathematics Studies, issue.82, 1974.

J. S. Birman and X. Lin, Knot polynomials and Vassiliev's invariants, Inventiones Mathematicae, vol.13, issue.1, pp.225-270, 1993.
DOI : 10.1007/BF01231287

P. Bellingeri and V. Bardakov, Groups of virtual and welded links, J. Knot Theory Ramifications, vol.23, p.1450014, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00687526

J. S. Carter, S. Kamada, and M. Saito, STABLE EQUIVALENCE OF KNOTS ON SURFACES AND VIRTUAL KNOT COBORDISMS, Journal of Knot Theory and Its Ramifications, vol.11, issue.03, pp.311-322, 2002.
DOI : 10.1142/S0218216502001639

S. Chmutov, S. Duzhin, and J. Mostovoy, Vassiliev knot invariants, 2012.

O. Chterental, Virtual braids and virtual curve diagrams, Journal of Knot Theory and Its Ramifications, vol.24, issue.13, 2014.
DOI : 10.1142/S0218216515410011

B. Cisneros, Virtual braids from a topological viewpoint, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00940106

P. Dehornoy, I. Dynnikov, D. Rolfsen, and B. Wiest, Ordering Braids, Mathematical Surveys and Monographs, vol.148, 2008.
DOI : 10.1090/surv/148
URL : https://hal.archives-ouvertes.fr/hal-00373521

E. Dies and A. Nicas, The center of the virtual braid group is trivial, Journal of Knot Theory and Its Ramifications, vol.23, issue.08, p.1450042, 2014.
DOI : 10.1142/S0218216514500424

T. Fiedler, Gauss diagram invariants for knots and links Mathematics and its Applications, pp.0-7923, 2001.

F. Th, A small state sum for knots, Topology, vol.32, issue.2, pp.281-294, 1993.

F. Th and A. Stoimenow, New knot and link invariants, Proceedings of the international conference on knot theory " Knots in Hellas Series on knots and everything 24, 2000.

P. Freyd, D. Yetter, J. Hoste, W. B. Lickorsh, K. C. Millett et al., A new polynomial invariant of knots and links, Bulletin of the American Mathematical Society, vol.12, issue.2, pp.239-246, 1985.
DOI : 10.1090/S0273-0979-1985-15361-3

A. Gaifullin and V. O. Manturov, ON THE RECOGNITION OF BRAIDS, Journal of Knot Theory and Its Ramifications, vol.11, issue.08, pp.1193-1209, 2002.
DOI : 10.1142/S0218216502002207

E. Godelle and L. Paris, K(??, 1) and word problems for infinite type Artin???Tits groups, and applications to virtual braid groups, Mathematische Zeitschrift, vol.26, issue.5, pp.3-4, 2012.
DOI : 10.1007/s00209-012-0989-9
URL : https://hal.archives-ouvertes.fr/hal-00498766

M. Goussarov, On n-equivlence of knots and invariants of finite degree English translation: Topology of manifolds and varieties, Wap. Nauchn. Sem. S-Peterburg. Otdel. Mat. Inst. Steklov (POMI) Adv. Soviet Math, vol.208, issue.18, pp.152-1763, 1993.

M. Goussarov, Finite type invariants are presented by Gauss diagram formulas, preprint (translated from Russian by O. Viro), 1998.

M. Goussarov, M. Polyak, and O. Viro, Finite-type invariants of classical and virtual knots, Topology, pp.1045-1068, 2000.

V. Jones, A polynomial invariant for knots via von Neumann algebras, Bulletin of the American Mathematical Society, vol.12, issue.1, pp.103-111, 1985.
DOI : 10.1090/S0273-0979-1985-15304-2

N. Kamada and S. Kamada, ABSTRACT LINK DIAGRAMS AND VIRTUAL KNOTS, Journal of Knot Theory and Its Ramifications, vol.09, issue.01, pp.93-106, 2000.
DOI : 10.1142/S0218216500000049

S. Kamada, Braid presentation of virtual knots and welded knots, Osaka J. Math, vol.44, pp.441-458, 2007.

L. Kauffman, Virtual Knots, talks at MSRI Meeting in, 1997.

L. H. Kauffman, Virtual Knot Theory, European Journal of Combinatorics, vol.20, issue.7, pp.663-690, 1999.
DOI : 10.1006/eujc.1999.0314

L. Kauffman and S. Lambropoulou, Virtual braids, Fundamenta Mathematicae, vol.184, pp.159-186
DOI : 10.4064/fm184-0-11

L. Kauffman and S. Lambropoulou, VIRTUAL BRAIDS AND THE L-MOVE, Journal of Knot Theory and Its Ramifications, vol.15, issue.06, pp.773-811, 2006.
DOI : 10.1142/S0218216506004750

L. Kauffman and S. Et-lambropoulou, A Categorical Structure for the Virtual Braid Group, Communications in Algebra, vol.9, issue.12, pp.4679-4704, 2011.
DOI : 10.1090/S1061-0022-2010-01112-9

L. Kauffman and S. Et-lambropoulou, A CATEGORICAL MODEL FOR THE VIRTUAL BRAID GROUP, Journal of Knot Theory and Its Ramifications, vol.21, issue.13, p.48, 2012.
DOI : 10.1142/S0218216512400081

C. Kassel and V. Turaev, Braid groups, Graduate Texts in Mathematics, vol.247, 2008.
DOI : 10.1007/978-0-387-68548-9

G. Kuperberg, What is a virtual link?, Algebraic & Geometric Topology, vol.3, issue.1, pp.587-591, 2003.
DOI : 10.2140/agt.2003.3.587

V. Lebed, Symmetric Categories as a Means of Virtualization for Braid Groups and Racks
URL : https://hal.archives-ouvertes.fr/hal-00709240

V. Lebed, Braided Objects: Unifying Algebraic Structures and Categorifying Virtual Braids, 2012.
URL : https://hal.archives-ouvertes.fr/tel-00775857

V. Lebed, CATEGORICAL ASPECTS OF VIRTUALITY AND SELF-DISTRIBUTIVITY, Journal of Knot Theory and Its Ramifications, vol.22, issue.09, p.1350045, 2013.
DOI : 10.1142/S0218216513500454

V. O. Manturov, Recognition of Virtual Braids, Russian) Zap. Nauchn. Sem. S.-Peterburg Geom. i, pp.131-5409, 2003.
DOI : 10.1007/s10958-005-0415-5

V. O. Manturov and D. P. Ilyutko, Virtual knots. The state of the art. Translated from the 2010 Russian original, Series on Knots and Everything, pp.978-981

H. R. Morton, Threading knot diagrams, Mathematical Proceedings of the Cambridge Philosophical Society, vol.82, issue.02, pp.247-260, 1986.
DOI : 10.1090/S0273-0979-1985-15304-2

K. Murasugi and B. Kurpita, A study of braids Mathematics and its Applications, pp.0-7923, 1999.

T. Ohtsuki, Quantum invariants. A study of knots, 3-manifolds, and Their Sets, 2001.

M. Polyak and O. Viro, Gauss diagram formulas for Vassiliev invariants , International Math, Research Notices, issue.11, pp.445-453, 1994.

A. Thiel, Cat??gorification des groupes de tresses virtuelles, Annales math??matiques Blaise Pascal, vol.18, issue.2, pp.231-243, 2011.
DOI : 10.5802/ambp.297

A. Thiel, VIRTUAL BRAID GROUPS OF TYPE B AND WEAK CATEGORIFICATION, Journal of Knot Theory and Its Ramifications, vol.21, issue.02, pp.1250020-1250041, 2012.
DOI : 10.1142/S0218216511009777
URL : https://hal.archives-ouvertes.fr/hal-01271583

P. Traczyk, A simple proof of Markov's theorem Knots in Poland, Proceedings of the Conference, pp.400-419, 1995.

V. Vershinin, ON HOMOLOGY OF VIRTUAL BRAIDS AND BURAU REPRESENTATION, Journal of Knot Theory and Its Ramifications, vol.10, issue.05, pp.795-812, 2001.
DOI : 10.1142/S0218216501001165

V. A. Vassiliev, Cohomology of knot spaces. Theory of singularities and its applications, Adv. Soviet Math. Math. Soc, pp.23-69, 1990.

M. Wada, Group invariants of links, Topology, vol.31, issue.2, pp.399-406, 1992.
DOI : 10.1016/0040-9383(92)90029-H