Given a link map f into a manifold of the form Q = N × ℝ, when can it be deformed to an “unlinked” position (in some sense, e.g. where its components map to disjoint ℝ-levels)? Using the language of normal bordism theory as well as the path space approach of Hatcher and Quinn we define obstructions , ε = + or ε = -, which often answer this question completely and which, in addition, turn out to distinguish a great number of different link homotopy classes. In certain cases they even allow a complete link homotopy classification. Our development parallels recent advances in Nielsen coincidence theory and also leads to the notion of Nielsen numbers of link maps. In the special case when N is a product of spheres sample calculations are carried out. They involve the homotopy theory of spheres and, in particular, James-Hopf invariants.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-12,
author = {Ulrich Koschorke},
title = {Linking and coincidence invariants},
journal = {Fundamenta Mathematicae},
volume = {184},
year = {2004},
pages = {187-203},
zbl = {1116.57021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-12}
}
Ulrich Koschorke. Linking and coincidence invariants. Fundamenta Mathematicae, Tome 184 (2004) pp. 187-203. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-12/