arXiv subjects

François Charette

Publications and source records attributed to François Charette.

4 recordsLinked to original sources

arXiv2017

Quantum Reidemeister torsion, open Gromov-Witten invariants and a spectral sequence of Oh

We adapt classical Reidemeister torsion to monotone Lagrangian submanifolds using the pearl complex of Biran and Cornea. The definition involves generic choices of data and we identify a class of Lagrangians for which this torsion is invariant and can be computed in terms of genus zero open Gromov-Witten invariants. This class is defined by a vanishing property of a spectral sequence of Oh in Lagrangian Floer theory.

math.SG↗

arXiv2016

On the cohomology ring of narrow Lagrangian 3-manifolds, quantum Reidemeister torsion, and the Landau-Ginzburg superpotential

Let $L$ be a closed, orientable, monotone Lagrangian 3-manifold of a symplectic manifold $(M, ω)$, for which there exists a local system such that the corresponding Lagrangian quantum homology vanishes. We show that its cohomology ring satisfies a certain dichotomy, which depends only on the parity of the first Betti number of $L$. Essentially, the triple cup product on the first cohomology group is shown to be either of maximal rank or identically zero. This in turn influences the Landau-Ginzburg superpotential of $L$: either one of its partial derivatives do not vanish on the corresponding local system, or it is globally constant. We use this to prove that quantum Reidemeister torsion is invariant and can be expressed in terms of open Gromov-Witten invariants of $L$.

math.SG↗

arXiv2015

Categorification of Seidel's representation

Two natural symplectic constructions, the Lagrangian suspension and Seidel's quantum representation of the fundamental group of the group of Hamiltonian diffeomorphisms, Ham(M), with (M,ω) a monotone symplectic manifold, admit categorifications as actions of the fundamental groupoid Π(Ham(M)) on a cobordism category recently introduced in \cite{Bi-Co:cob2} and, respectively, on a monotone variant of the derived Fukaya category. We show that the functor constructed in \cite{Bi-Co:cob2} that maps the cobordism category to the derived Fukaya category is equivariant with respect to these actions.

math.SG↗

arXiv2014

Gromov width and uniruling for orientable Lagrangian surfaces

We prove a conjecture of Barraud-Cornea for orientable Lagrangian surfaces. As a corollary, we obtain that displaceable Lagrangian 2--tori have finite Gromov width. In order to do so, we adapt the pearl complex of Biran-Cornea to the non-monotone situation based on index restrictions for holomorphic discs.

math.SG↗