Geodesic
All two dimensional links are null homotopic
Bartels, Arthur C1 ; Teichner, Peter1
1 University of California at San Diego, La Jolla, California 92093-0112, USA
Geometry & topology, Tome 3 (1999) no. 1, pp. 235-252.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We show that any number of disjointly embedded 2–spheres in 4–space can be pulled apart by a link homotopy, ie, by a motion in which the 2–spheres stay disjoint but are allowed to self-intersect.

DOI : 10.2140/gt.1999.3.235
Keywords: Link homotopy, Milnor group, concordance

Bartels, Arthur C 1 ; Teichner, Peter 1

1 University of California at San Diego, La Jolla, California 92093-0112, USA 
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Bartels, Arthur C; Teichner, Peter. All two dimensional links are null homotopic. Geometry & topology, Tome 3 (1999) no. 1, pp. 235-252. doi : 10.2140/gt.1999.3.235. http://geodesic.mathdoc.fr/articles/10.2140/gt.1999.3.235/

[1] A Bartels, Link homotopy in codimension two, PhD thesis, UC San Diego (1999)

[2] A K Bousfield, D M Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics 304, Springer (1972)

[3] T D Cochran, Link concordance invariants and homotopy theory, Invent. Math. 90 (1987) 635

[4] S Ferry, Homotoping $\varepsilon$–maps to homeomorphisms, Amer. J. Math. 101 (1979) 567

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

[6] R Fenn, D Rolfsen, Spheres may link homotopically in 4–space, J. London Math. Soc. $(2)$ 34 (1986) 177

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

[8] M Golubitsky, V Guillemin, Stable mappings and their singularities, Graduate Texts in Mathematics 14, Springer (1973)

[9] M A Kervaire, J W Milnor, Groups of homotopy spheres I, Ann. of Math. $(2)$ 77 (1963) 504

[10] P A Kirk, Link maps in the four sphere, from: "Differential topology (Siegen, 1987)", Lecture Notes in Math. 1350, Springer (1988) 31

[11] W Massey, D Rolfsen, Problem section, from: "Low-dimensional topology", London Mathematical Society Lecture Note Series 95, Cambridge University Press (1985)

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

[13] C P Rourke, Embedded handle theory, concordance and isotopy, from: "Topology of Manifolds (Proc. Inst., Univ. of Georgia, Athens, Ga., 1969)", Markham, Chicago, Ill. (1970) 431

[14] J Stallings, Homology and central series of groups, J. Algebra 2 (1965) 170

[15] P Teichner, Stratified Morse theory and link homotopy, in preparation

[16] P Teichner, Pulling apart 2–spheres in 4–space, preprint (1997)

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