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Some homotopy theoretical questions arising in Nielsen coincidence theory

100%

Koschorke U.

Banach Center Publications

2009

tom 85

nr 1

275-280

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

100%

Koschorke U.

Fundamenta Mathematicae

2004

tom 184

nr 1

187-203

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.

Ograniczanie wyników

1 Banach Center Publications

1 Fundamenta Mathematicae

2 Koschorke U.

1 2009

1 2004

Wyniki wyszukiwania

Some homotopy theoretical questions arising in Nielsen coincidence theory

Linking and coincidence invariants