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Concordance des nœuds de dimension 4

Published online by Cambridge University Press:  20 November 2018

Vincent Blanloeil  and
Osamu Saeki
Vincent Blanloeil
Affiliation:
Département de Mathématiques, Université Louis Pasteur Strasbourg-I, 7, rue René Descartes, 67084 Strasbourg Cedex, France e-mail: blanloeil@math.u-strasbg.fr
Osamu Saeki
Affiliation:
Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan e-mail: saeki@math.kyushu-u.ac.jp
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Résumé

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Nous démontrons que tous les plongements d’une variété compacte sans bord et simplement connexe de dimension quatre dans la sphère de dimension six sont concordants.

Abstract

Abstract

We prove that for a simply connected closed 4-dimensional manifold, its embeddings into the sphere of dimension 6 are all concordant to each other.

Keywords

57Q4557Q6057R4057R6557N13concordancecobordismenœud de dimension 4chirurgie plongée
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 4 , 01 December 2007 , pp. 481 - 485
Copyright
Copyright © Canadian Mathematical Society 2007

References

Références

[1] Barden, D., Simply connected five-manifolds. Ann. of Math. 82(1965), 365–385.Google Scholar
[2] Blanloeil, V. et Saeki, O., Cobordisme des surfaces plongées dans S 4 . Osaka J.Math. 42(2005), 751–765.Google Scholar
[3] Cappell, S. and Shaneson, J., Embeddings and immersions of four-dimensional manifolds in R 6 . Dans: Geometric Topology, Academic Press, New York, 1979, pp. 301–303.Google Scholar
[4] Erle, D., Quadratische Formen als Invarianten von Einbettungen der Kodimensio 2 Topology 8(1969), 99–114.Google Scholar
[5] Freedman, M., The topology of four-dimensional manifolds. J. Differential Geom. 17(1982), no. 3, 357–453.Google Scholar
[6] Kervaire, M. A., Les noeuds de dimensions supérieures. Bull. Soc. Math. France 93(1965), 225–271.Google Scholar
[7] Kotschick, D., Non-trivial harmonic spinors on certain algebraic surfaces. Dans: Einstein Metrics and Yang-Mills Connections. Lecture Notes in Pure and Appl. Math. 145, Dekker, New York, 1993, pp. 85–88.Google Scholar
[8] Kotschick, D., Orientations and geometrisations of compact complex surfaces. Bull. London Math. Soc. 29(1997), no. 2, 145–149.Google Scholar
[9] Milnor, J., Spin structures on manifolds. Enseignement Math. 9(1963), 198–203.Google Scholar
[10] Moishezon, B. and Teicher, M., Existence of simply connected algebraic surfaces of general type with positive and zero indices. Proc. Nat. Acad. Sci. U.S.A. 83(1986), no. 18, 6665–6666.Google Scholar
[11] Moishezon, B. and Teicher, M., Simply-connected algebraic surfaces of positive index. Invent. Math. 89(1987), no. 3, 601–643.Google Scholar
[12] Park, J., The geography of spin symplectic 4-manifolds. Math. Z. 240(2002), no. 2, 405–421.Google Scholar
[13] Ruberman, D., Imbedding four-manifolds and slicing links. Math. Proc. Cambridge Philos. Soc. 91(1982), no. 1, 107–110.Google Scholar
[14] Vogt, R., Cobordismus von Knoten. Dans: Knot Theory. Lecture Notes in Math. 685, Springer-Verlag, Berlin, 1978, pp. 218–226.Google Scholar
[15] Vogt, R., Cobordismus von hochzusammenhängenden Knoten. Dissertation, Rheinische Friedrich-Wilhelms-Universität, Bonn, 1978, Bonner Mathematische Schriften 116, Universität Bonn, Mathematisches Institut, Bonn, 1980.Google Scholar
[16] Wall, C. T. C., On simply-connected 4-manifolds. J. London Math. Soc. 39(1964), 141–149.Google Scholar
[17] Wallace, A. H., Modifications and cobounding manifolds. Canad. J. Math. 12(1960), 503–528.Google Scholar