Exponential separation in 4–manifolds

Krushkal, Vyacheslav S¹

¹ Department of Mathematics, Yale University, New Haven, Connecticut 06520-8283, USA

Geometry & topology, Tome 4 (2000) no. 1, pp. 397-405.

Résumé

We use a new geometric construction, grope splitting, to give a sharp bound for separation of surfaces in 4–manifolds. We also describe applications of this technique in link-homotopy theory, and to the problem of locating ${\pi }_1$–null surfaces in 4–manifolds. In our applications to link-homotopy, grope splitting serves as a geometric substitute for the Milnor group.

Détail

DOI : 10.2140/gt.2000.4.397

Keywords: 4–manifolds, gropes, $\pi_1$–null immersions, link homotopy

Bibliographie

[1] M H Freedman, The disk theorem for four-dimensional manifolds, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983)", PWN (1984) 647

[2] M H Freedman, X S Lin, On the $(A,B)$–slice problem, Topology 28 (1989) 91

[3] M H Freedman, F Quinn, Topology of 4–manifolds, Princeton Mathematical Series 39, Princeton University Press (1990)

[4] M H Freedman, P Teichner, 4–manifold topology I: Subexponential groups, Invent. Math. 122 (1995) 509

[5] R Kirby, A calculus for framed links in $S^3$, Invent. Math. 45 (1978) 35

[6] V S Krushkal, On the relative slice problem and four-dimensional topological surgery, Math. Ann. 315 (1999) 363

[7] V S Krushkal, F Quinn, Subexponential groups in 4–manifold topology, Geom. Topol. 4 (2000) 407

[8] V S Krushkal, P Teichner, Alexander duality, gropes and link homotopy, Geom. Topol. 1 (1997) 51

[9] J Milnor, Link groups, Ann. of Math. $(2)$ 59 (1954) 177