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Convex ribbon disks, quasipositivity, and Lagrangian sliceness
Abstract
We introduce a version of convex surface theory for immersed ribbon surfaces with Legendrian boundary. As an application, we establish a special case of K3: Problem 1.70 on sharpness in the slice-Bennequin inequality implying quasipositivity, and a special case of a conjecture of Cornwell, Ng, and Sivek on characterizing Lagrangian sliceness. Specifically, we prove that if K is a knot that bounds a "star-shaped" ribbon disk and satisfies sl̅(K) = −1 (resp.\ tb̅(K) = −1), then K is quasipositive (resp.\ Lagrangian slice). In fact, we prove these statements for any fixed transverse (resp.\ Legendrian) representative.
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BibTeX
@misc{breen2026convex,
title = {{Convex ribbon disks, quasipositivity, and Lagrangian sliceness}},
author = {Joseph Breen and Alexander Zupan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05331},
eprint = {2611.05331},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05331},
}
RIS
TY - UNPB
TI - Convex ribbon disks, quasipositivity, and Lagrangian sliceness
AU - Joseph Breen
AU - Alexander Zupan
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05331
UR - https://arxiv.org/abs/2611.05331
AB - We introduce a version of convex surface theory for immersed ribbon surfaces with Legendrian boundary. As an application, we establish a special case of K3: Problem 1.70 on sharpness in the slice-Bennequin inequality implying quasipositivity, and a special case of a conjecture of Cornwell, Ng, and Sivek on characterizing Lagrangian sliceness. Specifically, we prove that if K is a knot that bounds a "star-shaped" ribbon disk and satisfies sl̅(K) = −1 (resp.\ tb̅(K) = −1), then K is quasipositive (resp.\ Lagrangian slice). In fact, we prove these statements for any fixed transverse (resp.\ Legendrian) representative.
ER -