Work

Motion groups, Legendrian links, and non-trivial loops of embeddings

Year: 2026

Type: preprint

Abstract: We introduce, for an embedded Legendrian link~$L$ in a contact 3-manifold~$(M,ξ)$, the group of its \emph{Legendrian motions}. Analogously with the smooth case, we prove that this Legendrian motion group is isomorphic to the fundamental group of the space of unparametrised Legendrian embeddings. For all Legendrian knots in the standard contact 3-sphere, we characterise Legendrian motions in terms of contact mapping classes of the knot exterior. In an appendix, we give a short exposition of our techniques applied to the smooth case, comparing to the classical Dahm homomorphism.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.10804

Authors: Corrigan, Gabriel, Nonino, Isacco

Institution: University of Glasgow

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of Glasgow, College of Science and Engineering, University of Minnesota, Engineering and Physical Sciences Research Council

Award: DTP 2224 University of Glasgow

OpenAlex ID: W7221104728

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