Related papers: Coisotropic Submanifolds, Leafwise Fixed Points, a…

We exhibit two three-parameter families of locally conformal symplectic forms on the solvmanifold $M_{n,k}$ considered in [1], and show, using the Hodge-de Rham theory for the Lichnerowicz cohomology that that they are not $d_{\omega}$…

Let $\phi$ be a quadratic, monic polynomial with coefficients in $\mathcal O_{F,D}[t]$, where $\mathcal O_{F,D}$ is a localization of a number ring $\mathcal O_F$. In this paper, we first prove that if $\phi$ is non-square and…

A noncompact (oriented) surface satisfies the condition $(\star)$ if their isolated ends are ''accumulated by genus''. We show that every surface satisfying this condition is homeomorfic to the leaf of a minimal codimension one foliation on…

We give constraints on smooth families of 4-manifolds with boundary using Manolescu's Seiberg-Witten Floer stable homotopy type, provided that the fiberwise restrictions of the families to the boundaries are trivial families of 3-manifolds.…

We prove the Conley conjecture for a closed symplectically aspherical symplectic manifold: a Hamiltonian diffeomorphism of a such a manifold has infinitely many periodic points. More precisely, we show that a Hamiltonian diffeomorphism with…

In this paper we study the question of fragility and robustness of leafwise intersections of coisotropic submanifolds. Namely, we construct a closed hypersurface and a sequence of Hamiltonians $C^0$-converging to zero such that the…

A foliation $(M,\mathcal{F})$ is said to be $2$--calibrated if it admits a closed 2-form $\omega$ making each leaf symplectic. By using approximately holomorphic techniques, a sequence $W_k$ of $2$--calibrated submanifolds of…

The main goal of this paper is to give a unified treatment to many known cuplength estimates. As the base case, we prove that for $C^0$-perturbations of a function which is Morse-Bott along a closed submanifold, the number of critical…

Consider the cotangent bundle of a Riemannian manifold $(M,g)$ of dimension 2 or more, endowed with a twisted symplectic structure defined by a closed weakly exact 2-form $\sigma$ on $M$ whose lift to the universal cover of $M$ admits a…

We study coisotropic deformations of a compact regular coisotropic submanifold $C$ in a contact manifold $(M,\xi)$. Our main result states that $C$ is rigid among nearby coisotropic submanifolds whose characteristic foliation is…

The Nielsen Conjecture for Homeomorphisms asserts that any homeomorphism $f$ of a closed manifold is isotopic to a map realizing the Nielsen number of $f$, which is a lower bound for the number of fixed points among all maps homotopic to…

We prove that the higher harmonic signature of an even dimensional oriented Riemannian foliation of a compact Riemannian manifold with coefficients in a leafwise U(p,q)-flat complex bundle is a leafwise homotopy invariant. We also prove the…

We study the following rigidity problem in symplectic geometry:can one displace a Lagrangian submanifold from a hypersurface? We relate this to the Arnold Chord Conjecture, and introduce a refined question about the existence of relative…

This article announces a series of articles aiming at introducing the concept of symplectic spinors into symplectic topology resp. the concept of Frobenius structures. We will give lower bounds for the number of fixed points of a…

We show that the presence of a non-contractible one-periodic orbit of a Hamiltonian diffeomorphism of a connected closed symplectic manifold $(M,\omega)$ implies the existence of infinitely many non-contractible simple periodic orbits,…

The variational problem for the functional $F=\frac12\|\phi^*\omega\|_{L^2}^2$ is considered, where $\phi:(M,g)\to (N,\omega)$ maps a Riemannian manifold to a symplectic manifold. This functional arises in theoretical physics as the strong…

We describe the differential graded Lie algebras governing Poisson deformations of a holomorphic Poisson manifold and coisotropic embedded deformations of a coisotropic holomorphic submanifold. In both cases, under some mild additional…

It's known from from work of Hofer, Wysocki, and Zehnder [1996] and Bourgeois [2002] that in a contact manifold equipped with either a nondegenerate or Morse-Bott contact form, a finite-energy pseudoholomorphic curve will be asymptotic at…

In this paper we provide a complete characterisation of coisotropic embeddings of precosymplectic manifolds into cosymplectic manifolds. This result extends a theorem of Gotay about coisotropic embeddings of presymplectic manifolds. We also…

We investigate the stability of fibers of coisotropic fibrations on holomorphic symplectic manifolds and generalize Voisin's result on Lagrangian subvarieties to this framework. We present applications to the moduli space of holomorphic…