Legendrian fronts for affine varieties

Roger Casals, Emmy Murphy

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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 languageEnglish (US)
Pages (from-to)225-323
Number of pages99
JournalDuke Mathematical Journal
Volume168
Issue number2
DOIs
StatePublished - Feb 1 2019

ASJC Scopus subject areas

  • Mathematics(all)

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