Geometric and homotopy theoretic methods in Nielsen coincidence theory.
The rank of vector fields of Grassmannian manifolds
Multiple Points of Immersions, and the Kahn-Priddy Theorem.
Link maps and the geometry of their invariants.
Belts and k-invariants of link maps in spheres.
Concordance and Bordism of Line Fields.
On link maps and their homotopy classification.
Some homotopy theoretical questions arising in Nielsen coincidence theory
Basic examples show that coincidence theory is intimately related to central subjects of differential topology and homotopy theory such as Kervaire invariants and divisibility properties of Whitehead products and of Hopf invariants. We recall some recent results and ask a few questions which seem to be important for a more comprehensive understanding.
Linking and coincidence invariants
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...
Coincidence free pairs of maps
This paper centers around two basic problems of topological coincidence theory. First, try to measure (with the help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of coincidence free maps. Secondly, describe the set of loose pairs of homotopy classes. We give a brief (and necessarily very incomplete) survey of some old and new advances concerning the first problem. Then we attack the second problem mainly in the setting of homotopy...
Geometric interpretations of the generalized Hopf invariant.
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