Related papers: Special Lagrangians with Cylindrical Tangent Cones

We prove a number of results relating various measures (volume, Legendrian index, stability index, and spectral curve genus) of the geometric complexity of special Lagrangian $T^2$-cones. We explain how these results fit into a program to…

We construct a new infinite family of 4-dimensional isolated symplectic singularities with trivial local fundamental group, answering a question of Beauville raised in 2000. Three constructions are presented for this family: (1) as…

Locally homogeneous Lorentzian three-manifolds with recurrect curvature are special examples of Walker manifolds, that is, they admit a parallel null vector field. We obtain a full classification of the symmetries of these spaces, with…

We investigate deformations of lagrangian manifolds with singularities. We introduce a complex similar to the de Rham-complex whose cohomology calculates deformation spaces. Examples of singular lagrangian varieties are presented and…

We set up a topological framework for degenerations of symplectic manifolds into singular spaces paying a special attention to the behavior of Lagrangian manifolds and their (holomorphic) membranes. We show that degenerations into singular…

General Lagrangians are constructed for N=2 supersymmetric gauge theories in four space-time dimensions involving gauge groups with (non-abelian) electric and magnetic charges. The charges induce a scalar potential, which, when the charges…

These notes consist of a study of special Lagrangian submanifolds of Calabi-Yau manifolds and their moduli spaces. The particular case of three dimensions, important in string theory, allows us to introduce the notion of gerbes. These offer…

The SYZ Conjecture explains Mirror Symmetry between mirror Calabi-Yau 3-folds M,M' in terms of special Lagrangian fibrations f : M --> B and f' : M' --> B over the same base B, whose fibres are dual 3-tori, except for singular fibres. One…

This paper is a continuation of math.DG/0408005. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of S^n by looking at the conormal bundle of appropriate…

We find lower bounds on the number of intersection points between two relatively exact Hamiltonian isotopic Lagrangians. The bounds are given in terms of the cuplength of the Lagrangian in various multiplicative generalised cohomology…

Capacities that provide both qualitative and quantitative obstructions to the existence of a Lagrangian cobordism between two $(n-1)$-dimensional submanifolds in parallel hyperplanes of $\mathbb{R}^{2n}$ are defined using the theory of…

Motivated by $G_2$-manifolds with coassociative fibrations in the adiabatic limit, Donaldson and Scaduto conjectured the existence of associative submanifolds homeomorphic to a three-holed $3$-sphere with three asymptotically cylindrical…

In this note we study exceptional algebroids, focusing on their relation to type IIB superstring theory. We show that a IIB-exact exceptional algebroid (corresponding to the group $E_{n(n)}\times \mathbb{R}^+$, for $n\le 6$) locally has a…

We construct special Lagrangian 3-spheres in non-K\"ahler compact threefolds equipped with the Fu-Li-Yau geometry. These non-K\"ahler geometries emerge from topological transitions of compact Calabi-Yau threefolds. From this point of view,…

This paper is a follow-up to an earlier paper math.DG/0410260 on desingularizations of Calabi-Yau 3-folds with a conical singularity. In math.DG/0410260 we study Calabi-Yau 3-folds M_0 with a conical singularity at x modelled on some…

A second order family of special Lagrangian submanifolds of complex m-space is a family characterized by the satisfaction of a set of pointwise conditions on the second fundamental form. For example, the set of ruled special Lagrangian…

We construct a Lagrangian submanifold, inside the cotangent bundle of a real torus, which we call a Lagrangian pair of pants. It is given as the graph of the differential of a smooth function defined on the real blow up of a Lagrangian…

Let $(M, \om)$ be a symplectic manifold, endowed with a compatible almost complex structure J and the associated metric g . For any p \in {1, 2, ... (dim M)/2} the form $\Om := \frac{\om^p}{p!}$ is a calibration. More generally, dropping…

Lagrangian curves in 4-space entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic…

We consider various constructions of monotone Lagrangian submanifolds of $C P^n, S^2\times S^2$, and quadric hypersurfaces of $C P^n$. In $S^2\times S^2$ and $C P^2$ we show that several different known constructions of exotic monotone tori…