Existence and construction of non-loose knots

Anubhav Mukherjee; Hyunki Min; John B. Etnyre; Rima Chatterjee

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Existence and construction of non-loose knots

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arxiv 2310.04908 v1 pith:MWVIYLCM submitted 2023-10-07 math.GT math.SG

Rima Chatterjee , John B. Etnyre , Hyunki Min , Anubhav Mukherjee This is my paper · ORCID

classification math.GTmath.SG

keywords non-looseconditionsunderadmitcablingclassifyconstructioncontact

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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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