Linking and coincidence invariants

Ulrich Koschorke. "Linking and coincidence invariants." Fundamenta Mathematicae 184.1 (2004): 187-203. <http://eudml.org/doc/282593>.

@article{UlrichKoschorke2004,
abstract = {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.},
author = {Ulrich Koschorke},
journal = {Fundamenta Mathematicae},
keywords = {Link homotopy invariant; normal bordism; Nielsen number},
language = {eng},
number = {1},
pages = {187-203},
title = {Linking and coincidence invariants},
url = {http://eudml.org/doc/282593},
volume = {184},
year = {2004},
}

TY - JOUR
AU - Ulrich Koschorke
TI - Linking and coincidence invariants
JO - Fundamenta Mathematicae
PY - 2004
VL - 184
IS - 1
SP - 187
EP - 203
AB - 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.
LA - eng
KW - Link homotopy invariant; normal bordism; Nielsen number
UR - http://eudml.org/doc/282593
ER -