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Fabio Gironella

Publications and source records attributed to Fabio Gironella.

16 recordsLinked to original sources
arXiv2026

Fillability obstructions for high-dimensional confoliations

In this paper, we study confoliations in dimensions higher than three mostly from the perspective of symplectic fillability. Our main result is that Massot-Niederkrüger-Wendl's bordered Legendrian open book, an object that obstructs the weak symplectic fillability of contact manifolds, admits a generalization for confoliations equipped with symplectic data. Applications include the non-fillability of the product of an overtwisted contact manifold and a class of symplectic manifolds, and the fact that Bourgeois contact structures associated with overtwisted contact manifolds admit no weak symplectic fillings for which the symplectic structure restricts at the boundary to a positive generator of the second cohomology of the torus factor. In addition, along the lines of the original 3-dimensional work of Eliashberg and Thurston, we give a new definition of approximation and deformation of confoliations by contact structures and describe some natural examples.

math.SG↗
arXiv2026

Tight contact structures without symplectic fillings are everywhere

We show that for all $n \ge 3$, any $(2n+1)$-dimensional manifold that admits a tight contact structure, also admits a tight but non-fillable contact structure, in the same almost contact class. For $n=2$, we obtain the same result, provided that the first Chern class vanishes. We further construct Liouville but not Weinstein fillable contact structures on any Weinstein fillable contact manifold of dimension at least $7$ with torsion first Chern class.

math.SG↗
arXiv2026

$C^0$-Poisson geometry, coisotropic submanifolds, and clean intersection points

In this work, we initiate the study of rigidity and non-rigidity phenomena for Poisson homeomorphisms, defined as uniform $C^0$-limits of Poisson diffeomorphisms. First, we prove that Poisson homeomorphisms preserve the singular symplectic foliation: they map symplectic leaves to symplectic leaves by symplectic homeomorphisms. Second, we establish the $C^0$-rigidity of coisotropic submanifolds in Poisson manifolds. A key ingredient is the notion of ''clean intersection point'' between a submanifold and the leaves of a singular foliation, whose study is of independent interest for singular foliation theory and Poisson geometry. In contrast with the symplectic case, characteristic foliations of coisotropic submanifolds are not rigid under Poisson homeomorphisms, exhibiting flexibility phenomena specific to the Poisson setting. We discuss partial rigidity results, introduce a topological invariant of coisotropic submanifolds, the $C^0$-characteristic partition, and show that $C^0$-coisotropic submanifolds are non-smooth objects whose vanishing ideal defines a Lie subalgebra of the Poisson algebra. Finally, we consider Poisson homeomorphisms that lift to symplectic homeomorphisms of a symplectic realization and show that nearly all Poisson manifolds admit non-liftable Poisson homeomorphisms. Our main results answer three questions posed by Joksimović and Mărcuţ.

math.SG↗
arXiv2025

Non-density results in high dimensional stable Hamiltonian topology

We push forward the study of higher dimensional stable Hamiltonian topology by establishing two non-density results. First, we prove that stable hypersurfaces are not $C^3$-dense in any isotopy class of embedded hypersurfaces on any ambient symplectic manifold of dimension $2n\geq 8$. Our second result is that on any manifold of dimension $2m+1\geq 5$, the set of non-degenerate stable Hamiltonian structures is not $C^2$-dense among stable Hamiltonian structures in any given stable homotopy class that satisfies a mild assumption. The latter generalizes a result by Cieliebak and Volkov to arbitrary dimensions.

math.SG↗
arXiv2025

Vanishing cycles of symplectic foliations

Several results in recent years have shown that the usual generalizations of taut foliations to higher dimensions, based only on topological concepts, lead to a theory that lacks the complexity of its 3-dimensional counterpart. Instead, we propose strong symplectic foliations as natural candidates for such a generalization and we prove in this article that they do yield some interesting rigidity results, such as potentially topological obstructions on the underlying ambient manifold. We introduce a high-dimensional generalization of 3-dimensional vanishing cycles for symplectic foliations, which we call Lagrangian vanishing cycles, and prove that they prevent a symplectic foliation from being strong, just as vanishing cycles prevent tautness in dimension 3 due to the classical result of Novikov from 1964. We then describe, in every codimension, examples of symplectically foliated manifolds which admit Lagrangian vanishing cycles, but for which more classical arguments fail to obstruct strongness. In codimension 1, this is achieved by a rather explicit modification of the symplectic foliation, which allows us to open up closed leaves having non-trivial holonomy on both sides, and is thus of independent interest. Since there is no comprehensive source on holomorphic curves with boundary in symplectic foliations, we also give a detailed introduction to much of the analytic theory, in the hope that it might serve as a reference for future work in this direction.

math.SG↗
arXiv2024

Operator-Projected Variational Quantum Imaginary Time Evolution

Variational Quantum Imaginary Time Evolution (VQITE) is a leading technique for ground state preparation on quantum computers. A significant computational challenge of VQITE is the determination of the quantum geometric tensor. We show that requiring the imaginary-time evolution to be correct only when projected onto a chosen set of operators allows to achieve a twofold reduction in circuit depth by bypassing fidelity estimations, and reduces measurement complexity from quadratic to linear in the number of parameters. We demonstrate by a simulation of the transverse-field Ising model that our algorithm achieves a several orders of magnitude improvement in the number of measurements required for the same accuracy.

quant-ph↗
arXiv2022

Bourgeois contact structures: tightness, fillability and applications

Given a contact structure on a manifold $V$ together with a supporting open book decomposition, Bourgeois gave an explicit construction of a contact structure on $V \times \mathbb{T}^2$. We prove that all such structures are universally tight in dimension $5$, independent on whether the original contact manifold is itself tight or overtwisted. In arbitrary dimensions, we provide obstructions to the existence of strong symplectic fillings of Bourgeois manifolds. This gives a broad class of new examples of weakly but not strongly fillable contact $5$-manifolds, as well as the first examples of weakly but not strongly fillable contact structures in all odd dimensions. These obstructions are particular instances of more general obstructions for $\mathbb S^1$-invariant contact manifolds. We also obtain a classification result in arbitrary dimensions, namely that the unit cotangent bundle of the $n$-torus has a unique symplectically aspherical strong filling up to diffeomorphism.

math.SG↗
arXiv2022

Asymptotically holomorphic theory for symplectic orbifolds

We extend Donaldson's asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a symplectic orbifold such that the symplectic form defines an integer cohomology class, we prove that there exist sections of large tensor powers of the prequantizable line bundle such that their zero sets are symplectic suborbifolds. We then derive a Lefschetz hyperplane theorem for these suborbifolds, that computes their real cohomology up to middle dimension. We also get the hard Lefschetz and formality properties for them, when the ambient manifold satisfies those properties.

math.SG↗
arXiv2021

Exact orbifold fillings of contact manifolds

We study exact orbifold fillings of contact manifolds using Floer theories. Motivated by Chen-Ruan's orbifold Gromov-Witten invariants, we define symplectic cohomology of an exact orbifold filling as a group using classical techniques, i.e. choosing generic almost complex structures. By studying moduli spaces of pseudo-holomorphic/Floer curves in orbifolds, we obtain various non-existence, restrictions and uniqueness results for orbifold singularities of exact orbifold fillings of many contact manifolds. For example, we show that exact orbifold fillings of $(\mathbb{RP}^{2n-1},ξ_{\mathrm{std}})$ always have exactly one singularity modeled on $\mathbb{C}^n/(\mathbb{Z}/2\mathbb{Z})$ if $n\ne 2^k$. Lastly, we show that in dimension at least $3$ there are pairs of contact manifolds without exact cobordisms in either direction, and that the same holds for exact orbifold cobordisms in dimension at least $5$.

math.SG↗
arXiv2021

Existence of conformal symplectic foliations on closed manifolds

We consider the existence of symplectic and conformal symplectic codimension-one foliations on closed manifolds of dimension at least 5. Our main theorem, based on a recent result by Bertelson-Meigniez, states that in dimension at least 7 any almost contact structure is homotopic to a conformal symplectic foliation. In dimension 5 we construct explicit conformal symplectic foliations on every closed, simply-connected, almost contact manifold, as well as honest symplectic foliations on a large subset of them. Lastly, via round-connected sums, we obtain, on closed manifolds, examples of conformal symplectic foliations which admit a linear deformation to contact structures.

math.SG↗
arXiv2021

Examples of symplectic non-leaves

This paper deals with the following question: which manifolds can be realized as leaves of codimension-1 symplectic foliations on closed manifolds? We first observe that leaves of symplectic foliations are necessarily strongly geometrically bounded. We show that a symplectic structure which admits an exhaustion by compacts with (convex) contact boundary can be deformed to a strongly geometrically bounded one. We then give examples of smooth manifolds which admit a strongly geometrically bounded symplectic form and can be realized as a smooth leaf, but not as a symplectic leaf for any choice of symplectic form on them. Lastly, we show that the (complex) blowup of 2n-dimensional Euclidean space at infinitely many points, both admits strongly geometrically bounded symplectic forms for which it can and cannot be realized as a symplectic leaf.

math.SG↗
arXiv2019

On some examples and constructions of contact manifolds

The first goal of this paper is to construct examples of higher dimensional contact manifolds with specific properties. Our main results in this direction are the existence of tight virtually overtwisted closed contact manifolds in all dimensions and the fact that every closed contact 3-manifold, which is not (smoothly) a rational homology sphere, contact--embeds with trivial normal bundle inside a hypertight closed contact 5-manifold. This uses known construction procedures by Bourgeois (on products with tori) and Geiges (on branched covering spaces). We pass from these procedures to definitions; this allows to prove a uniqueness statement in the case of contact branched coverings, and to study the global properties (such as tightness and fillability) of the results of both constructions without relying on any auxiliary choice in the procedures. A second goal allowed by these definitions is to study relations between these constructions and the notions of supporting open book, as introduced by Giroux, and of contact fiber bundle, as introduced by Lerman. For instance, we give a definition of Bourgeois contact structures on flat contact fiber bundles which is local, (strictly) includes the results of the Bourgeois construction, and allows to recover an isotopy class of supporting open books on the fibers. This last point relies on a reinterpretation, inspired by an idea by Giroux, of supporting open books in terms of pairs of contact vector fields.

math.SG↗
arXiv2019

A remark on the contactomorphism group of overtwisted contact spheres

We show the existence of elements of infinite order in some homotopy groups of the contactomorphism group of overtwisted spheres. It follows in particular that the contactomorphism group of some high dimensional overtwisted spheres is not homotopically equivalent to a finite dimensional Lie group.

math.SG↗
arXiv2019

5-dimensional Bourgeois contact structures are tight

Given a contact structure on a manifold $V$ together with a supporting open book decomposition, Bourgeois gave an explicit construction for a contact structure on $V \times \mathbb{T}^2$. We prove that all such structures are universally tight in dimension $5$, independent on whether the original contact manifold is tight or overtwisted.

math.SG↗