PreprintCC BY 4.0arXiv
Decomposable concordances induce closed immersions
Abstract
We show that a decomposable Lagrangian concordance between two Legendrian links must induce a closed immersion between the sheaf moduli of its ends. As the main application of this criterion, we prove a conjecture of Cornwell-Ng-Sivek, showing that their Lagrangian concordance is not decomposable. This establishes the first known example of a regular Lagrangian concordance between Legendrian knots that is not decomposable. In addition, we show that even the simpler Lagrangian concordance, satelliting via the Reeb 2-copy, is not decomposable.
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BibTeX
@misc{casals2026decomposable,
title = {{Decomposable concordances induce closed immersions}},
author = {Roger Casals},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03448},
eprint = {2611.03448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03448},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Decomposable concordances induce closed immersions
AU - Roger Casals
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03448
UR - https://arxiv.org/abs/2611.03448
AB - We show that a decomposable Lagrangian concordance between two Legendrian links must induce a closed immersion between the sheaf moduli of its ends. As the main application of this criterion, we prove a conjecture of Cornwell-Ng-Sivek, showing that their Lagrangian concordance is not decomposable. This establishes the first known example of a regular Lagrangian concordance between Legendrian knots that is not decomposable. In addition, we show that even the simpler Lagrangian concordance, satelliting via the Reeb 2-copy, is not decomposable.
ER -