Related papers: The Weinstein conjecture for stable Hamiltonian st…

We study the contact geometry of the connected components of the energy hypersurface, in the symmetric restricted 3-body problem on $\mathbb{S}^2$, for a specific type of motion of the primaries. In particular, we show that these components…

We show that an overtwisted contact structure on a closed, oriented 3-manifold can be defined by a contact form having a Bott-integrable Reeb flow if and only if the Poincar\'e dual of its Euler class is represented by a graph link.

Using lattice homology, we give an explicit combinatorial description of the Seiberg-Witten-Floer spectrum $\mathit{SWF}(Y)$ for $Y$ an almost-rational plumbed homology sphere. This class of manifolds includes all Seifert fibered rational…

Using Heegaard Floer homology, we construct a numerical invariant for any smooth, oriented $4$-manifold $X$ with the homology of $S^1 \times S^3$. Specifically, we show that for any smoothly embedded $3$-manifold $Y$ representing a…

We define symplectic fractional twists, which generalize Dehn twists, and use these in open books to investigate contact structures. The resulting contact structures are invariant under a circle action, and share several similarities with…

We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong…

A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, which is called a real structure. A real contact 3-manifold is a real 3-manifold with a contact distribution that is antisymmetric with…

We find a geometric invariant of isotopy classes of strongly irreducible Heegaard splittings of toroidal 3-manifolds. Combining this invariant with a theorem of R Weidmann, proved here in the appendix, we show that a closed, totally…

Let $M^n$ be either a simply connected space form or a rank-one symmetric space of noncompact type. We consider Weingarten hypersurfaces of $M\times\mathbb R$, which are those whose principal curvatures $k_1,\dots ,k_n$ and angle function…

We say that a Riemannian manifold M has rank at least k if every geodesic in M admits at least k parallel Jacobi fields. The Rank Rigidity Theorem of Ballmann and Burns-Spatzier, later generalized by Eberlein-Heber, states that a complete,…

Consider the cotangent bundle of a closed Riemannian manifold and an almost complex structure close to the one induced by the Riemannian metric. For Hamiltonians which grow for instance quadratically in the fibers outside of a compact set,…

In this article, we study the growth rate of Reeb orbits on fiberwise star-shaped hypersurfaces in the cotangent bundle of a closed manifold. We prove that under a suitable topological condition on the base manifold the Reeb flow on any…

We use instanton gauge theory to prove that if $Y$ is a closed, orientable $3$-manifold such that $H_1(Y;\mathbb{Z})$ is nontrivial and either $2$-torsion or $3$-torsion, and if $Y$ is neither $\#^r \mathbb{RP}^3$ for some $r\geq 1$ nor…

Let $\mathcal{F} $ be a pointwise almost periodic decomposition of a compact metrizable space $X$. Then $\mathcal{F} $ is $R$-closed if and only if $\hat{\mathcal{F}} $ is usc. Moreover, if there is a finite index normal subgroup $H$ of an…

We study the monopole Floer homology of a SOLV rational homology sphere Y from the point of view of spectral theory. Applying ideas of Fourier analysis on solvable groups, we show that for suitable SOLV metrics on Y, small regular…

We consider a closed three-dimensional contact sub-Riemannian manifold. The objective of this note is to provide a precise description of the sub-Riemannian geodesics with large initial momenta: we prove that they "spiral around the Reeb…

We study stability properties of the topological entropy of Reeb flows on contact 3-manifolds with respect to the C^0-distance on the space of contact forms. Our main results show that a C^\infty-generic contact form on a closed co-oriented…

We determine the local equivalence class of the Seiberg-Witten Floer stable homotopy type of a spin rational homology 3-sphere $Y$ embedded into a spin rational homology $S^{1} \times S^{3}$ with a positive scalar curvature metric so that…

We characterize the universal covering of connected analytic pseudo-Riemannian manifolds which admit a non-trivial and isometric action of the simple Lie group $SL(3,\mathbb{R})$ with a dense orbit preserving a finite volume. If such…

In this article we give a sharp upper bound on the possible values of the Euler characteristic for a minimal symplectic filling of a tight contact structure on a lens space. This estimate is obtained by looking at the topology of the spaces…