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Classification of Legendrian doubles and suspensions
Abstract
We define a construction of Legendrians inside contact manifolds that arise by doubling an exact Lagrangian filling in the page of an open book decomposition. This can be seen as a generalization of a previous construction by Courte and Ekholm to arbitrary open books. These Legendrians, called Legendrian doubles, are shown to admit regular flexible exact Lagrangian fillings, and they are thus classified up to Legendrian isotopy by classical data. Finally, we show that the Legendrian suspension construction, as defined by Arikan and the author in previous work,-this is a Legendrian contained inside a page of an open book that is obtained by using Seidel's suspension of Lefschetz fibrations- is a Legendrian double.
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BibTeX
@misc{yildirim2026classification,
title = {{Classification of Legendrian doubles and suspensions}},
author = {Yasemin Yildirim},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08557},
eprint = {2609.08557},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08557},
}
RIS
TY - UNPB
TI - Classification of Legendrian doubles and suspensions
AU - Yasemin Yildirim
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08557
UR - https://arxiv.org/abs/2609.08557
AB - We define a construction of Legendrians inside contact manifolds that arise by doubling an exact Lagrangian filling in the page of an open book decomposition. This can be seen as a generalization of a previous construction by Courte and Ekholm to arbitrary open books. These Legendrians, called Legendrian doubles, are shown to admit regular flexible exact Lagrangian fillings, and they are thus classified up to Legendrian isotopy by classical data. Finally, we show that the Legendrian suspension construction, as defined by Arikan and the author in previous work,-this is a Legendrian contained inside a page of an open book that is obtained by using Seidel's suspension of Lefschetz fibrations- is a Legendrian double.
ER -