TY - JOUR
T1 - Legendrian fronts for affine varieties
AU - Casals, Roger
AU - Murphy, Emmy
N1 - Funding Information:
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.
Funding Information:
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.
Publisher Copyright:
© 2019.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - 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.
AB - 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.
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U2 - 10.1215/00127094-2018-0055
DO - 10.1215/00127094-2018-0055
M3 - Article
AN - SCOPUS:85061752142
SN - 0012-7094
VL - 168
SP - 225
EP - 323
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 2
ER -