The Connectivity Order of Links
St\'ephane Dugowson (LISMMA)
TL;DR
This paper introduces the connectivity order as a new numerical invariant for links based on their splittability properties, and proves that every finite connectivity structure can be realized by a link.
Contribution
It defines the connectivity order for links and proves the Brunn-Debrunner-Kanenobu Theorem relating finite connectivity structures to links.
Findings
Connectivity order as a new invariant for links
Proof that every finite connectivity structure can be realized by a link
Introduction of a connectivity space framework for links
Abstract
We associate at each link a connectivity space which describes its splittability properties. Then, the notion of order for finite connectivity spaces results in the definition of a new numerical invariant for links, their connectivity order. A section of this short paper presents a theorem which asserts that every finite connectivity structure can be realized by a link : the Brunn-Debrunner-Kanenobu Theorem.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research