Linking and coincidence invariants

• Autorzy: Ulrich Koschorke
• Języki publikacji: EN

Abstrakty

EN

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 $ω̃_{ε}(f)$, 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 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.

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 57Q45: Knots and links (in high dimensions)
• 55P35: Loop spaces
• 55S35: Obstruction theory
• 57R90: Other types of cobordism
• 55Q25: Hopf invariants
• 55Q45: Stable homotopy of spheres

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 184
• Numer: 1
• Strony: 187-203

Daty

wydano

2004

Twórcy

autor

Ulrich Koschorke

• Universität Siegen, Emmy Noether Campus, Walter-Flex-Str. 3, D-57068 Siegen, Germany

Identyfikatory

DOI

10.4064/fm184-0-12