TL;DR
This paper demonstrates the existence of a universal transverse link in the standard contact 3-sphere, over which all contact 3-manifolds can be realized as branched covers, revealing a unifying structure in contact topology.
Contribution
It introduces a specific transverse link that serves as a universal branched cover base for all contact 3-manifolds, a novel concept in contact topology.
Findings
Existence of a universal transverse link in the standard contact 3-sphere.
All contact 3-manifolds are contact branched covers over this link.
Provides a new perspective on the structure of contact 3-manifolds.
Abstract
We show that there exists a transverse link in the standard contact structures on the 3-sphere such that all contact 3-manifolds are contact branched covers over this transverse link.
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