Products and connected sums of spheres as monotone Lagrangian submanifolds

Abstract

We obtain topological restrictions on Maslov classes of monotone Lagrangian submanifolds of C n . We also construct families of new examples of monotone Lagrangian submanifolds, which show that the restrictions on Maslov classes are sharp in certain cases. Contents 1. Introduction 1 Acknowledgements 4 2. Preliminaries 4 2.1. Local Floer cohomology 4 2.2. Spectral sequences of the Floer algebra 5 3. Main theorems: the existence part 6 4. Main theorems: the restriction part 11 5. Some explicit examples of monotone submanifolds of C n 15 6. Monotone Lagrangian submanifolds of CP n 16 References 18

Non-isotopic monotone Lagrangian submanifolds of $\mathbb{C}^n$

“…The construction allows us to find the Maslov class of Lagrangians. Moreover, in certain cases our examples realize all possible minimal Maslov numbers ( see [8] for more details).…”

“…We know that R × D Γ T Γ → T 2 = T Γ /D Γ is a fibration, where the fiber is R. It is proved in [8] that under our assumptions (n, p, k are even) the fibration is trivial and is diffepmorphic to where…”

“…In papers [7], [8], new monotone Lagrangian submanifolds of C n are constructed and their minimal Maslov numbers are found. Using Oh's spectral sequence, some restrictions on minimal Maslov numbers of the constructed Lagrangians are obtained.…”