Yasemin Yildirim | Searcharxiv

arXiv2026

Classification of Legendrian doubles and suspensions

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.

math.SG↗

arXiv2024

Compatible Relative Lefschetz Fibrations On Admissible Relative Stein Pairs

For more than two decades it has been known that any compact Stein surface (of real dimension four) admits a compatible Lefschetz fibration over a two-disk. More recently, Giroux and Pardon have generalized this result by giving a complex geometric proof for the existence of compatible Lefschetz fibrations on Stein domains of any even dimension. As a preparatory step in proving the former, Akbulut and Ozbagci have shown that there exist infinitely many pairwise non-equivalent Lefschetz fibrations on the four-ball by using a result of Lyon constructing fibrations on the complements of (p,q)-torus links in the three-sphere. In this paper, we first extend this result to obtain compatible Lefschetz fibrations on the six-ball whose pages are (p, q, 2)-Brieskorn varieties, and then construct a compatible 'relative' Lefschetz fibrations on any Stein domain (of dimension six) which admit a certain ('admissible') 'relative Stein pair' structure. In particular, we provide a purely topological proof for the existence of Lefschetz fibrations on specific 6-dimensional Stein domains.

math.GT↗