E. Artin, Zur Isotopie zweidimensionaler Fl??chen imR 4, Abhandlungen aus dem Mathematischen Seminar der Universit??t Hamburg, vol.4, issue.1, pp.174-177, 1925.
DOI : 10.1007/BF02950724

B. Audoux, On the welded Tube map. to appear in Contemp, Math. of the AMS, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01066617

B. Audoux, P. Bellingeri, J. Meilhan, and E. Wagner, On usual, virtual and welded knotted objects up to homotopy, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01176073

D. Bar-natan and Z. Dancso, Finite-type invariants of w-knotted objects, I: w-knots and the Alexander polynomial, Algebraic & Geometric Topology, vol.16, issue.2, 2014.
DOI : 10.2140/agt.2016.16.1063

D. Bar-natan and Z. Dancso, Finite type invariants of w-knotted objects II: Tangles, foams and the Kashiwara-Vergne problem. arXiv e-prints:1405, 1955.

V. G. Bardakov, The virtual and universal braids, Fundamenta Mathematicae, vol.184, pp.1-18, 2004.
DOI : 10.4064/fm184-0-1

A. Bartels and P. Teichner, All two dimensional links are null homotopic, Geometry & Topology, vol.3, issue.1, pp.235-252, 1999.
DOI : 10.2140/gt.1999.3.235

T. E. Brendle and A. Hatcher, Configuration spaces of rings and wickets, Commentarii Mathematici Helvetici, vol.88, issue.1, pp.131-162, 2013.
DOI : 10.4171/CMH/280

J. 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

J. S. Carter and M. Saito, Knotted surfaces and their diagrams, volume 55 of Mathematical Surveys and Monographs, 1998.

D. T. Cochran, Link concordance invariants and homotopy theory, Inventiones Mathematicae, vol.66, issue.3, pp.635-645, 1987.
DOI : 10.1007/BF01389182

H. A. Dye and L. H. Kauffman, VIRTUAL HOMOTOPY, Journal of Knot Theory and Its Ramifications, vol.19, issue.07, pp.935-960, 2010.
DOI : 10.1142/S0218216510008200

R. Fenn, R. Rimányi, and C. Rourke, The braid-permutation group, Topology, vol.36, issue.1, pp.123-135, 1997.
DOI : 10.1016/0040-9383(95)00072-0

R. Fenn and D. Rolfsen, Spheres May Link Homotopically in 4-Space, Journal of the London Mathematical Society, vol.2, issue.1, pp.177-184, 1986.
DOI : 10.1112/jlms/s2-34.1.177

T. Fiedler, Gauss diagram invariants for knots and links, volume 532 of Mathematics and its Applications, 2001.

R. Fox and J. W. Milnor, Singularities of 2-spheres in 4-space and cobordism of knots, Osaka J. Math, vol.3, pp.257-267, 1966.

R. H. Fox, Some problems in knot theory In Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, N.J, pp.168-176, 1961.

M. Goussarov, M. Polyak, and O. Viro, Finite-type invariants of classical and virtual knots, Topology, vol.39, issue.5, pp.1045-1168, 2000.
DOI : 10.1016/S0040-9383(99)00054-3

N. Habegger and X. Lin, The classification of links up to link-homotopy, Journal of the American Mathematical Society, vol.3, issue.2, pp.389-419, 1990.
DOI : 10.1090/S0894-0347-1990-1026062-0

N. Habegger and X. Lin, On Link Concordance and Milnor's ?? Invariants, Bulletin of the London Mathematical Society, vol.30, issue.4, pp.419-428, 1998.
DOI : 10.1112/S0024609398004494

N. Habegger and G. Masbaum, The Kontsevich integral and Milnor???s invariants, Topology, vol.39, issue.6, pp.1253-1289, 2000.
DOI : 10.1016/S0040-9383(99)00041-5

N. Habegger and J. Meilhan, On the Classification of Links up to Finite Type, Topology and Physics, pp.138-150, 2008.
DOI : 10.1142/9789812819116_0005

URL : https://hal.archives-ouvertes.fr/hal-00347808

A. Ichimori and T. Kanenobu, RIBBON TORUS KNOTS PRESENTED BY VIRTUAL KNOTS WITH UP TO FOUR CROSSINGS, Journal of Knot Theory and Its Ramifications, vol.21, issue.13, p.1240005, 2012.
DOI : 10.1142/S0218216512400056

T. Kanenobu and A. Shima, Two filtrations of ribbon 2-knots, Proceedings of the First Joint Japan-Mexico Meeting in Topology (Morelia, pp.143-168, 1999.
DOI : 10.1016/S0166-8641(01)00115-8

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

M. Kervaire and J. W. Milnor, ON 2-SPHERES IN 4-MANIFOLDS, Proc. Natl. Acad. Sci. USA, pp.1651-1657, 1961.
DOI : 10.1073/pnas.47.10.1651

M. A. Kervaire, Les n??uds de dimensions sup??rieures, Bulletin de la Société mathématique de France, vol.79, pp.225-271, 1965.
DOI : 10.24033/bsmf.1624

P. Kirk, Link homotopy with one codimension two component, Transactions of the American Mathematical Society, vol.319, issue.2, pp.663-688, 1990.
DOI : 10.1090/S0002-9947-1990-0970268-X

U. Koschorke, A generalization of Milnor's ??-invariants to higher-dimensional link maps, Topology, vol.36, issue.2, pp.301-324, 1997.
DOI : 10.1016/0040-9383(96)00018-3

Y. Kotorii, THE MILNOR $\bar{\mu}$ INVARIANTS AND NANOPHRASES, Journal of Knot Theory and Its Ramifications, vol.22, issue.02, pp.1250142-2013
DOI : 10.1142/S0218216512501428

O. Kravchenko and M. Polyak, Diassociative Algebras and Milnor???s Invariants for Tangles, Letters in Mathematical Physics, vol.11, issue.7, pp.297-316, 2011.
DOI : 10.1007/s11005-010-0459-4

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

G. Li, An invariant of link homotopy in dimension four, Topology, vol.36, pp.881-897, 1997.

J. Milnor, Link Groups, The Annals of Mathematics, vol.59, issue.2, pp.177-195, 1954.
DOI : 10.2307/1969685

J. Milnor, Isotopy of links Algebraic geometry and topology. In A symposium in honor of S. Lefschetz, pp.280-306, 1957.

M. Polyak, -invariants, Algebraic & Geometric Topology, vol.5, issue.4, pp.1471-1479, 2005.
DOI : 10.2140/agt.2005.5.1471

URL : https://hal.archives-ouvertes.fr/insu-00653315

M. Polyak and O. Viro, Gauss diagram formulas for Vassiliev invariants, 445ff., approx. 8 pp. (electronic), 1994.

D. Roseman, Reidemeister-type moves for surfaces in four-dimensional space, Knot theory, pp.347-380, 1995.

S. Satoh, VIRTUAL KNOT PRESENTATION OF RIBBON TORUS-KNOTS, Journal of Knot Theory and Its Ramifications, vol.09, issue.04, pp.531-542, 2000.
DOI : 10.1142/S0218216500000293

J. Stallings, Homology and central series of groups, Journal of Algebra, vol.2, issue.2, pp.170-181, 1965.
DOI : 10.1016/0021-8693(65)90017-7

S. Suzuki, Knotting problems of 2-spheres in 4-sphere, Math. Sem. Notes Kobe Univ, vol.4, issue.3, pp.241-371, 1976.

V. Turaev, Lectures on topology of words, Japanese Journal of Mathematics, vol.54, issue.1, pp.1-39, 2007.
DOI : 10.1007/s11537-007-0634-2

D. S. Magnus and A. Karrass, Combinatorial group theory, XIII of Pure and Appl. Math. Interscience, 1966.

T. Yajima, On the fundamental groups of knotted 2-manifolds in the 4-space, J. Math. Osaka City Univ, vol.13, pp.63-71, 1962.

T. Yajima, On simply knotted spheres in R 4, Osaka J. Math, vol.1, pp.133-152, 1964.

T. Yanagawa, On ribbon 2-knot: The 3-manifold bounded by the 2-knots, Osaka J. Math, vol.6, pp.447-464, 1969.

T. Yanagawa, On ribbon 2-knots II: The second homotopy group of the complementary domain, Osaka J. Math, vol.6, pp.465-473, 1969.

T. Yanagawa, On Ribbon 2-knots III: On the unknotting Ribbon 2-knots in S 4, Osaka J. Math, vol.7, pp.165-172, 1970.

A. Yasuhara, Classification of string links up to self delta-moves and concordance, Algebraic & Geometric Topology, vol.9, issue.1, pp.265-275, 2009.
DOI : 10.2140/agt.2009.9.265