A Lagrangian sphere which is not a vanishing cycle
- 67 Downloads
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.
- 4.Donaldson, S.: Polynomials, vanishing cycles and Floer homology. In: Arnold, V., Atiyah, M., Lax, P., Mazur, B. (eds.) Mathematics: Frontiers and Perspectives, The American Mathematical Monthly, pp. 55–64. American Mathematical Society, Providence (2000)Google Scholar
- 6.Miranda, R.: The basic theory of elliptic surfaces. Dottorato di Ricerca in Matematica. ETS Editrice, Pisa (1989)Google Scholar
- 8.Sheridan, N., Smith, I.: Symplectic topology of K3 surfaces via mirror symmetry. math.SG. arXiv:1709.09439