PreprintCC BY 4.0arXiv
Motion groups, Legendrian links, and non-trivial loops of embeddings
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.
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BibTeX
@misc{corrigan2026motion,
title = {{Motion groups, Legendrian links, and non-trivial loops of embeddings}},
author = {Gabriel Corrigan and Isacco Nonino},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10804},
eprint = {2610.10804},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10804},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Motion groups, Legendrian links, and non-trivial loops of embeddings
AU - Gabriel Corrigan
AU - Isacco Nonino
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10804
UR - https://arxiv.org/abs/2610.10804
AB - 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.
ER -