New lower bounds on the number of intersections of monotone Lagrangian submanifolds

Keddari, Nassima

doi:10.1090/tran/7640

New lower bounds on the number of intersections of monotone Lagrangian submanifolds
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Trans. Amer. Math. Soc. 376 (2023), 753-772 Request permission

Abstract:

Considering a closed monotone Lagrangian submanifold $L,$ we give, under some hypotheses, a lower bound on the intersection number of $L$ with its image by a generic Hamiltonian isotopy. First for monotone Lagrangian submanifolds $L$ which are $\mathbf {K}(\pi ,1)$ and, in particular, for monotone Lagrangian submanifolds with negative sectional curvature this bound is 1+$\beta _{1}(L).$ In more general cases the lower bound is weaker. We generalise some results previously obtained by L. Buhovsky in [J. Topol. Anal. 2 (2010), pp. 57–75] and P. Biran and O. Cornea in [Geom. Topol. 13 (2009), pp. 2881–2989].

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