The contact mapping class group and rational unknots in lens spaces
Hyunki Min
TL;DR
This paper classifies the contact mapping class group of lens spaces with standard contact structures and uses convex surface theory to classify Legendrian and transverse rational unknots up to isotopy.
Contribution
It provides a complete description of the contact mapping class group and classifies rational unknots in lens spaces, advancing understanding of contact topology in these manifolds.
Findings
Contact mapping class group of lens spaces determined
Legendrian and transverse rational unknots classified
Convex surface theory applied to classify knots
Abstract
We determine the contact mapping class group of the standard contact structures on lens spaces. To prove the main result, we use the one-parametric convex surface theory to classify Legendrian and transverse rational unknots in any tight contact structure on lens spaces up to Legendrian and transverse isotopy.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Numerical Analysis Techniques · Geometric Analysis and Curvature Flows