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Twist tori and pseudo toric structures
Symplectic Geometry · Submitted 15 Apr 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Below we show that any twist torus $\Theta^k \subset \R^{2k+2}$, defined in [1], can be constructed via pseudo toric considerations.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Twist tori are examples of exotic monotone lagrangian tori, presented in [1]. | background 0.99 | 0.17 | 0.04 | asserted 1.00 |
| s1 | This tree of examples grew up over the first one --- the torus $\Theta \in \R^4$, constructured in [2] and [3]. | background 1.00 | 0.14 | 0.03 | asserted 0.99 |
| s2 | On the other hand, in [4] and [5] we proposed a new structure which generalizes the notion of toric structure. | contribution 0.68 | 0.81 | 0.04 | asserted 1.00 |
| s3 | 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. | contribution 0.54 | 0.59 | 0.07 | asserted 0.99 |
| s4 | Below we show that any twist torus $\Theta^k \subset \R^{2k+2}$, defined in [1], can be constructed via pseudo toric considerations. | result 0.56 | 0.90 | 0.74 | asserted 1.00 |
| s5 | Due to this one can explicitly show that every $\Theta^k \subset \R^{2k+2}$ is displaceable. | result 0.97 | 0.89 | 0.28 | asserted 1.00 |
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The paper
Original 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.
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