Twist tori and pseudo toric structures

TL;DR

This paper demonstrates that twist tori, exotic monotone Lagrangian tori in symplectic geometry, can be constructed using pseudo toric structures, leading to the conclusion that all such twist tori are displaceable.

Contribution

It shows that twist tori can be realized via pseudo toric structures, providing explicit constructions and proving their displaceability.

Findings

All twist tori in ^{2k+2} are displaceable.

Pseudo toric structures can generate known exotic Lagrangian tori.

Explicit construction of twist tori via pseudo toric considerations.

Abstract

Twist tori are examples of exotic monotone lagrangian tori, presented in [1]. This tree of examples grew up over the first one --- the torus $\Theta \in \R^4$, constructured in [2] and [3]. On the other hand, in [4] and [5] we proposed a new structure which generalizes the notion of toric structure. One calls this generalization pseudo toric structure, and several examples were given which show that certain toric symplectic manifolds can carry the structre and that certain non toric symplectic manifolds do the same. Below we show that any twist torus $\Theta^k \subset \R^{2k+2}$, defined in [1], can be constructed via pseudo toric considerations. Due to this one can explicitly show that every $\Theta^k \subset \R^{2k+2}$ is displaceable.