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F. Pasquotto

Publications and source records attributed to F. Pasquotto.

4 recordsLinked to original sources
arXiv2020

Bounds for tentacular Hamiltonians

This paper represents a first step towards the extension of the definition of Rabinowitz Floer homology to non-compact energy hypersurfaces in exact symplectic manifolds. More concretely, we study under which conditions it is possible to establish $L^{\infty}$-bounds for the Floer trajectories of a Hamiltonian with non-compact energy levels. Moreover, we introduce a class of Hamiltonians, called tentacular Hamiltonians, which satisfy the conditions: how to define RFH for these examples will be the subject of a follow-up paper.

math.SG↗
arXiv2014

On periodic orbits in cotangent bundles of non-compact manifolds

This paper is concerned with the existence of periodic orbits on energy hypersurfaces in cotangent bundles of Riemannian manifolds defined by mechanical Hamiltonians. In \cite{bpv} it was proved that, provided certain geometric assumptions are satisfied, regular mechanical hypersurfaces in $\mathbb{R}^{2n}$, in particular non-compact ones, contain periodic orbits if one homology group among the top half does not vanish. In the present paper we extend the above mentioned existence result to a class of hypersurfaces in cotangent bundles of Riemannian manifolds with flat ends.

math.SG↗
arXiv2009

Desingularisation of orbifolds obtained from symplectic reduction at generic coadjoint orbits

We show how to construct a resolution of symplectic orbifolds obtained as quotients of presymplectic manifolds with a torus action. As a corollary, this allows us to desingularise generic symplectic quotients. Given a manifold with a Hamiltonian action of a compact Lie group, symplectic reduction at a coadjoint orbit which is transverse to the moment map produces a symplectic orbifold. If moreover the points of this coadjoint orbit are regular elements of the Lie coalgebra, that is, their stabiliser is a maximal torus, the result for torus quotients may be applied to obtain a desingularisation of these symplectic orbifolds. Regular elements of the Lie coalgebra are generic in the sense that the singular strata have codimension at least three. Additionally, we show that even though the result of a symplectic cut is an orbifold, it can be modified in an arbitrarily small neighbourhood of the cut hypersurface to obtain a smooth symplectic manifold.

math.SG↗