Existence and construction of non-loose knots
Rima Chatterjee, John B. Etnyre, Hyunki Min, Anubhav Mukherjee
TL;DR
This paper establishes criteria for the existence of non-loose Legendrian and transverse knots in overtwisted contact structures, classifies non-loose rational unknots in lens spaces, and explores how non-looseness behaves under cabling.
Contribution
It provides necessary and sufficient conditions for non-loose knots, classifies all non-loose rational unknots in lens spaces, and analyzes the preservation of non-looseness under cabling.
Findings
Criteria for non-loose Legendrian and transverse knots
Classification of non-loose rational unknots in lens spaces
Conditions for non-looseness preservation under cabling
Abstract
In this paper we give necessary and sufficient conditions for a knot type to admit non-loose Legendrian and transverse representatives in some overtwisted contact structure, classify all non-loose rational unknots in lens spaces, and discuss conditions under which non-looseness is preserved under cabling.
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Taxonomy
TopicsGeometric and Algebraic Topology