arXiv subjects

Charlotte Kirchhoff-Lukat

Publications and source records attributed to Charlotte Kirchhoff-Lukat.

5 recordsLinked to original sources

arXiv2026

Coisotropic branes in symplectic manifolds

A brane in a symplectic manifold is a coisotropic submanifold $Y$ endowed with a compatible closed 2-form $F$, which together induce a transverse complex structure. For a specific class of branes we give an explicit description of branes nearby a given one, and for arbitrary branes we describe the infinitesimal deformations and provide an associated cochain complex. As an application, we determine to what extent coisotropic submanifolds near a given brane admit brane structures.

math.SG↗

arXiv2025

Moduli spaces of spacefilling branes in symplectic 4-manifolds

On a symplectic manifold $(M, ω)$, a spacefilling brane structure is a closed 2-form $F$ which determines a complex structure, with respect to which $F +iω$ is holomorphic symplectic. For holomorphic symplectic compact Kähler 4-manifolds, we show that the moduli space of spacefilling branes is smooth, and determine its dimension. The proof relies on the local Torelli theorem for K3 surfaces and tori.

math.SG↗

arXiv2025

Log Floer cohomology for oriented log symplectic surfaces

This article provides the first extension of Lagrangian Intersection Floer cohomology to Poisson structures which are almost everywhere symplectic, but degenerate on a lowerdimensional submanifold. The main result of the article is the definition of Lagrangian intersection Floer cohomology, referred to as log Floer cohomology, for orientable surfaces equipped with log symplectic structures. We show that this cohomology is invariant under suitable isotopies and that it is isomorphic to the log de Rham cohomology when computed for a single Lagrangian.

math.SG↗

arXiv2019

Natural lifts of Dorfman brackets

In this note we prove that, for a vector bundle $E$ over a manifold $M$, a Dorfman bracket on $TM\oplus E^*$ anchored by $\operatorname{pr}_{TM}$ and with $E$ a vector bundle over $M$, is equivalent to a lift from $Γ(TM\oplus E^*)$ to linear sections of $TE\oplus T^*E\to E$, that intertwines the given Dorfman bracket with the Courant-Dorfman bracket on sections of $TE\oplus T^*E$. This shows a universality of the Courant-Dorfman bracket, and allows us to caracterise twistings and symmetries of transitive Dorfman brackets via the corresponding lifts.

math.DG↗

arXiv2019

Lagrangian branes with boundary and symplectic methods for stable generalized complex manifolds

Generalized complex (GC) geometry interpolates between ordinary symplectic and complex geometry. Stable generalized complex manifolds (first introduced by Cavalcanti, Gualtieri in 2015) carry a Poisson structure which is generically symplectic, but degenerates on a (real) codimension-2 submanifold. Up to gauge equivalence, the stable generalized complex structure is thus determined by what is called an elliptic symplectic form, which allows the extension of a number of techniques and results from symplectic geometry to stable GC geometry. This paper introduces a new type of submanifold in stable GC manifolds: Lagrangian branes with boundary, which are generically Lagrangian and intersect the degeneracy locus in their boundary. By relating stable GC manifolds to log symplectic manifolds, we are able to prove results on local neighbourhoods and small deformations of such branes. We further investigate stable generalized complex Lefschetz fibrations, where Lagrangian branes with boundary arise as Lefschetz thimbles. These objects are thus expected to be part of a Fukaya category for stable GC manifolds, which we hope to develop in future work and which would allow the application of Floer theory techniques to a larger class of manifolds.

math.DG↗