# Seidel's morphism of toric 4-manifolds

@article{Anjos2014SeidelsMO, title={Seidel's morphism of toric 4-manifolds}, author={S{\'i}lvia Anjos and R'emi Leclercq}, journal={arXiv: Symplectic Geometry}, year={2014} }

Following McDuff and Tolman's work on toric manifolds [McDT06], we focus on 4-dimensional NEF toric manifolds and we show that even though Seidel's elements consist of infinitely many contributions, they can be expressed by closed formulas. From these formulas, we then deduce the expression of the quantum homology ring of these manifolds as well as their Landau-Ginzburg superpotential. We also give explicit formulas for the Seidel elements in some non-NEF cases. These results are closely…

## 6 Citations

### Loops in the fundamental group of Symp ( CP 2 # 5 CP 2 , ω ) which are not represented by circle actions ∗

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- 2022

We study generators of the fundamental group of the group of symplectomorphisms Symp(CP2#5CP2, ω) for some particular symplectic forms. It was observed by J. Kȩdra in [13] that there are many…

### Non-injectivity of Seidel's morphism

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The main purpose of this note is to exhibit a Hamiltonian diffeomorphism loop undetected by the Seidel morphism of certain 2-point blow-ups of $S^2 \times S^2$, only one of which being monotone. As…

### Noncontractible Hamiltonian loops in the kernel of Seidel’s representation

- Mathematics
- 2017

The main purpose of this note is to exhibit a Hamiltonian diffeomorphism loop undetected by the Seidel morphism of certain 2-point blow-ups of $S^2 \times S^2$, exactly one of which being monotone.…

### THE FUNDAMENTAL GROUP OF Symp(S × S2#4CP)

- Mathematics
- 2019

This report concerns the work done under the guidance of professor Sílvia Anjos for the 2019 edition of the Gulbenkian project Novos Talentos em Matemática. In a succint way, the starting point was…

### Loops in the fundamental group of $\mathrm{Symp} (\mathbb C\mathbb P^2\#\,5\overline{ \mathbb C\mathbb P}\,\!^2)$ which are not represented by circle actions

- Mathematics
- 2019

We study the generators of the fundamental group of the group of symplectomorphisms $\mathrm{Symp} (\mathbb C\mathbb P^2\#\,5\overline{ \mathbb C\mathbb P}\,\!^2, \omega)$ for some particular…

### Lagrangian Circle Actions

- Mathematics
- 2013

We consider paths of Hamiltonian diffeomorphism preserving a given compact monotone Lagrangian in a symplectic manifold that extend to an $S^1$--Hamiltonian action. We compute the leading term of the…

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