arXiv subjects

Aleksandra Marinkovic

Publications and source records attributed to Aleksandra Marinkovic.

3 recordsLinked to original sources

arXiv2025

On the existence of Hamiltonian 4-manifolds with a contact type boundary

While the Hamiltonian group actions on closed symplectic manifolds have been widely explored throughout the last couple of decades, the study on Hamiltonian group actions on symplectic manifolds with a contact type boundary has started only recently, with the work by Niederkrüger and the author [MN]. In this note we pursue this study by presenting several methods to construct such Hamiltonian circle manifolds in dimension 4.

math.SG↗

arXiv2016

On displaceability of pre-Lagrangian fibers in contact toric manifolds

In this note we analyze displaceability of pre-Lagrangian toric fibers in contact toric manifolds. While every symplectic toric manifold contains at least one non-displaceable Lagrangian toric fiber and infinitely many displaceable ones, we show that this is not the case for contact toric manifolds. More precisely, we prove that for the contact toric manifolds $\mathbb{S}^{2d-1} (d\geq 2)$ and $\mathbb{T}^k \times \mathbb{S}^{2d+k-1} (d \geq 1)$ all pre-Lagrangian toric fibers are displaceable, and that for all contact toric manifolds for which the toric action is free, except possibly non-trivial $\mathbb{T}^3$-bundles over $\mathbb{S}^2$, all pre-Lagrangian toric fibers are non-displaceable. Moreover we also prove that if for a compact connected contact toric manifold all but finitely many pre-Lagrangian toric fibers are non-displaceable then the action is necessarily free. On the other hand, as we will discuss, displaceability of all pre-Lagrangian toric fibers seems to be related to the non-orderability of the underlying contact manifolds.

math.SG↗

arXiv2016

Symplectic fillability of toric contact manifolds

According to Lerman, compact connected toric contact 3-manifolds with a non-free toric action whose moment cone spans an angle greater than $π$ are overtwisted, thus non-fillable. In contrast, we show that all compact connected toric contact manifolds in dimension greater than three are weakly symplectically fillable and most of them are strongly symplectically fillable. The proof is based on the Lerman's classification of toric contact manifolds and on our observation that the only contact manifolds in higher dimensions that admit free toric action are the cosphere bundle of $T^d, d\geq3$ $(T^d\times S^{d-1})$ and $T^2\times L_k,$ $k\in\mathbb{N},$ with the unique contact structure.

math.SG↗