Related papers: Geometrie affine Geometrie symplectique

Braverman, Finkelberg and Nakajima introduced the generalized affine Grassmannian slices $\overline{\mathcal W}^{\lambda}_{\mu}$ and showed that they are Coulomb branches of $3d$ $\mathcal N=4$ gauge theories. We prove a conjecture of…

By applying Seifert's algorithm to a special alternating diagram of a link L, one obtains a Seifert surface F of L. We show that the support of the sutured Floer homology of the sutured manifold complementary to F is affine isomorphic to…

We use symplectic cohomology to study the non-uniqueness of symplectic structures on the smooth manifolds underlying affine varieties. Starting with a Lefschetz fibration on such a variety and a finite set of primes, the main new tool is a…

Let $\mathcal{L}$ be a finite-dimensional semisimple Lie algebra of rank $N$ over an algebraically closed field of characteristic $0$. Associated to $\mathcal{L}$ is a family of polynomial folding maps…

Let L be a D-dimensional submanifold of a 2D-dimensional exact symplectic manifold (M, w) and let f be a symplectic diffeomorphism onf M. In this article, we deal with the link between the dynamics of f restricted to L and the geometry of L…

We give a simple proof that, for a pre-quantized compact symplectic manifold with a Lagrangian torus fibration, its Riemann-Roch number coincides with its number of Bohr-Sommerfeld fibres. This can be viewed as an instance of the…

We introduce and investigate a novel notion of transversely affine foliation, comparing and contrasting it to the previous ones in the literature. We then use it to give an extension of the classic Hadamard's theorem from Riemannian…

This note proves the geodesic completeness of any compact manifold endowed with a linear connection such that the closure of its holonomy group is compact.

We prove that the only exact Lagrangian submanifolds in an ALE space are spheres. ALE spaces are the simply connected hyperkahler manifolds which at infinity look like C^2/G for any finite subgroup G of SL(2,C). They can be realized as the…

In a recent paper, it was claimed that any homogeneous Finsler space of odd dimension admits a homogeneous geodesic through any point. For the proof, the algebraic method dealing with the reductive decomposition of the Lie algebra of the…

Friedman and Morgan made the "speculation" that deformation equivalence and diffeomorphism should coincide for algebraic surfaces. Counterexamples, for the hitherto open case of surfaces of general type, have been given in the last years by…

To classify the classical field theories with W-symmetry one has to classify the symplectic leaves of the corresponding W-algebra, which are the intersection of the defining constraint and the coadjoint orbit of the affine Lie algebra if…

We prove the strong Weinstein conjecture for closed contact manifolds that appear as the concave boundary of a symplectic cobordism admitting an essential local foliation by holomorphic spheres.

We study the geometry of the leaf closure space of regular and singular Riemannian foliations. We give conditions which assure that this leaf space is a singular symplectic or K\"ahler space.

We found some Lagrangian submanifolds of the adjoint semisimple orbit in two cases. For the first, the compact case, also known as the Generalized flag manifolds, we prove that the real flags can be seen as infinitesimally tight Lagrangian…

We show that closed aspherical manifolds supporting an affine structure, whose holonomy map is injective and contains a pure translation, must have vanishing simplicial volume. This provides some further evidence for the veracity of the…

We give a characterization of flat affine connections on manifolds by means of a natural affine representation of the universal covering of the Lie group of diffeomorphisms preserving the connection. From the infinitesimal point of view,…

Let M be a compact oriented even-dimensional manifold. This note constructs a compact symplectic manifold S of the same dimension and a map f from S to M of strictly positive degree. The construction relies on two deep results: the first is…

We prove that any coadjoint orbit with real eigenvalues of a complex semisimple Lie group, equipped with the real part of the canonical holomorphic symplectic form, is symplectomorphic to the cotangent bundle of a (partial) flag manifold.…

The purpose of the notes is to reiterate and expand the viewpoint, outlined in the paper math.AG/0110142 of T. Coates and the author, which recasts the concept of Frobenius manifold in terms of linear symplectic geometry and exposes the…