Unlinking information from 4-manifolds
Matthias Nagel, Brendan Owens
TL;DR
This paper extends existing theorems to multi-component links, allowing the calculation of unlinking numbers for certain prime links using advanced topological tools.
Contribution
It generalizes key unlinking theorems to multi-component links and completes the unlinking number classification for prime links with up to nine crossings.
Findings
Unlinking numbers for all nonsplit prime links with ≤9 crossings determined.
Extended theorems applicable to links with multiple components.
Applied linking forms, Floer correction terms, and Donaldson's theorem in new contexts.
Abstract
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.
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