Abstract
In this article we study Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. First, we provide a systematic recipe for translating from a Weinstein Lefschetz bifibration to a Legendrian handlebody. Then we present several new applications of this technique to symplectic topology. This includes the detection of flexibility and rigidity for several families of Weinstein manifolds and the existence of closed, exact Lagrangian submanifolds. In particular, we prove that the Koras-Russell cubic is Stein deformation-equivalent to ℂ 3 , and we verify the affine parts of the algebraic mirrors of two Weinstein 4-folds.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 225-323 |
| Number of pages | 99 |
| Journal | Duke Mathematical Journal |
| Volume | 168 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 1 2019 |
Funding
We are grateful to Y. Eliashberg, M. McLean, O. Plamenevskaya, and L. Traynor for valuable discussions. Special thanks go to A. Keating, K. Siegel, L. Starkston, and U. Varolgünes, whose many good comments have improved the quality of this article.We also thank D. Auroux, Y. Lekili, and F. Presas for comments on the initial draft. Finally, thanks are due the referees, whose detailed and thorough work has made this article better. Casals's work was partially supported by National Science Foundation (NSF) grant DMS-1608018 and a Fundación BBVA Research Fellowship. Murphy's work was partially supported by NSF grant DMS-1510305 and a Sloan Research Fellowship. Casals’s work was partially supported by National Science Foundation (NSF) grant DMS-1608018 and a Fundación BBVA Research Fellowship. Murphy’s work was partially supported by NSF grant DMS-1510305 and a Sloan Research Fellowship.
ASJC Scopus subject areas
- General Mathematics