2004/08/03 by Ulrich Koschorke, Koschorke, Ulrich
Mathematics · #55M20 #55M55 #55P35 #55P55 #55Q25 #55Q45 #55Q45 (Secondary) #55Q55 #55Q57 (Primary) #55S35 #55S57 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.GT #msc:55M20 #msc:55M55 #msc:55P35 #msc:55P55 #msc:55Q25 #msc:55Q45 #msc:55Q55 #msc:55Q57 #msc:55S35 #msc:55S57
paper · pdf · doi:10.48550/arxiv.math/0408046
16 pages
arxiv created 2004/08/03 · arxiv updated 2009/12/01
Given a link map f into a manifold of the form Q = N × \Bbb R, when can it be deformed to an unlinked position (in some sense, e.g. where its components map to disjoint \Bbb R-levels) ? Using the language of normal bordism theory as well as the path space approach of Hatcher and Quinn we define obstructions \widetildeωε(f), 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 leads also 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.