论文信息 - LINK MAPS IN ARBITRARY MANIFOLDS AND THEIR HOMOTOPY INVARIANTS

LINK MAPS IN ARBITRARY MANIFOLDS AND THEIR HOMOTOPY INVARIANTS

In this paper we generalize Milnor's μ-invariants of classical links to certain ("κ-Brunnian") higher dimensional link maps into fairly arbitrary manifolds. Our approach involves the homotopy theory of configuration spaces and of wedges of spheres. We discuss the strength of these invariants and their compatibilities e.g. with (Hilton decompositions of) linking coefficients. Our results suggest, in particular, a conjecture about possible new link homotopies.

U. Koschorke

[1] U. Kaiser. Link Theory in Manifolds , 1997 .

[2] U. Koschorke. A generalization of Milnor's μ-invariants to higher-dimensional link maps , 1997 .

[3] W. Kazez. Link homotopy in simply connected 3-manifolds , 1996 .

[4] U. Koschorke. On link maps and their homotopy classification , 1990 .

[5] P. Kirk. Link homotopy with one codimension two component , 1990 .

[6] U. Koschorke. Link maps and the geometry of their invariants , 1988 .

[7] D. Rolfsen,et al. Spheres May Link Homotopically in 4‐Space , 1986 .

[8] D. Puppe. Homotopiemengen und ihre induzierten Abbildungen. I , 1958 .

[9] Peter Hilton,et al. On the Homotopy Groups of the Union of Spheres , 1955 .

[10] Mathematische,et al. Symmetric surgery and boundary link maps , 1998 .

[11] Uwe Kaiser,et al. Link homotopy in the 2-metastable range , 1998 .

[12] U. Koschorke. Link homotopy with many components , 1991 .

[13] J. Levine. An approach to homotopy classification of links , 1988 .

[14] D. Hacon. Embeddings of Sp in S1 x Sq in the metastable range , 1968 .