A Lagrangian sphere which is not a vanishing cycle

  • François GreerEmail author


We give examples of Calabi–Yau threefolds containing Lagrangian spheres which are not vanishing cycles of nodal degenerations, answering a question of Donaldson in the negative.



The author is grateful to Mark McLean for suggesting the problem, and to the anonymous referees for valuable comments. He has also benefitted from communications with Denis Auroux, Jonathan Evans, Ivan Smith, Richard Thomas, and Abigail Ward.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Simons Center for Geometry and Physics, Stony Brook UniversityStony BrookUSA

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