1,452 research outputs found
Unlinking information from 4-manifolds
We generalise theorems of Cochran-Lickorish and Owens-Strle to the case of
links with more than one component. This enables the use of linking forms on
double branched covers, Heegaard Floer correction terms, and Donaldson's
diagonalisation theorem to complete the table of unlinking numbers for nonsplit
prime links with crossing number nine or less.Comment: 18 pages, 2 figures. V2: Improved exposition incorporating referee's
suggestions. Accepted for publication in Bull. London Math. So
Linking and coincidence invariants
Given a link map f into a manifold of the form Q = N \times \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 \widetilde\omega_\epsilon (f), \epsilon = + or \epsilon =
-, 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.Comment: 16 page
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