Related papers: Visualizing overtwisted discs in open books

The spaces of configurations of non-$k$-overlapping discs have been studied as a bimodule over the little discs operad. In fact, the spaces form a filtered operad. We define and study the induced structure on the homology.

A contact manifold admittting a supporting contact form without contractible Reeb orbits is called hypertight. In this paper we construct a Rabinowitz Floer homology associated to an arbitrary supporting contact form for a hypertight…

We construct examples in any odd dimension of contact manifolds with finite and non-zero algebraic torsion (in the sense of Latschev-Wendl), which are therefore tight and do not admit strong symplectic fillings. We prove that Giroux torsion…

Twisted vertex operators based on rational lattices have had many applications in vertex operator algebra theory and conformal field theory. In this paper, ``relativized'' twisted vertex operators are constructed in a general context based…

We give an elementary topological obstruction for a manifold $M$ of dimension $2q{+}1 \geq 7$ to admit a contact open book with flexible Weinstein pages and $c_1(\pi_2(M)) = 0$: if the torsion subgroup of the $q$-th integral homology group…

We give a sufficient condition using the Ozsv\'ath-Stipsicz-Szab\'o concordance invariant Upsilon for the monodromy of the open book decomposition of a fibered knot to be right-veering. As an application, we generalize a result of Baker on…

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…

In many applications it is important to establish if a given topological preordered space has a topology and a preorder which can be recovered from the set of continuous isotone functions. Under antisymmetry this property, also known as…

In this paper, we introduce the notions of an iterated planar Lefschetz fibration and an iterated planar open book decomposition and prove the Weinstein conjecture for contact manifolds supporting an open book that has iterated planar…

We show that if a contact open book $(\Sigma,h)$ on a $(2n+1)$-manifold $M$ ($n\geq1$) is induced by a Lefschetz fibration $\pi:W \to D^2$, then there is a one-to-one correspondence between positive stabilizations of $(\Sigma,h)$ and…

We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…

Using a combination of Atiyah-Segal ideas on one side and of Connes and Baum-Connes ideas on the other, we prove that the Twisted geometric K-homology groups of a Lie groupoid have an external multiplicative structure extending hence the…

We build handle decompositions of n-manifolds that encode given open book decompositions and describe handle slides that reveal new open book decompositions on the same underlying manifold, for $n \geq 3$. This recovers known stabilization…

We give a short alternative proof of Honda-Kazec-Matic's result, which states that a fibered knot with pseudo-Anosov monodromy and fractional Dehn twist coefficient $\geq1$ supports a contact structure that is a perturbation of a taut…

It is conjectured that for every convex disks K, the translative covering density of K and the lattice covering density of K are identical. It is well known that this conjecture is true for every centrally symmetric convex disks. For the…

We show that one can achieve transversality for lifts of holomorphic disks to a projectivized vector bundle by locally enlarging the structure group and considering the action of gauge transformations on the almost complex structure, which…

We prove that in dimension 3 every nondegenerate contact form is carried by a broken book decomposition. As an application we get that if M is a closed irreducible oriented 3-manifold that is not a graph manifold, for example a hyperbolic…

In this paper we prove that the closed $4$-ball admits non-K\"ahler complex structures with strictly pseudoconcave boundary. Moreover, the induced contact structure on the boundary $3$-sphere is overtwisted.

We describe the structure of hyperelliptic Rauzy diagrams and hyperelliptic Rauzy-Veech groups. In particular, this provides a solution of the hyperelliptic cases of a conjecture of Zorich on the Zariski closure of Rauzy-Veech groups.

We introduce a variant of contact homology for convex open contact manifolds. As an application, we prove the existence of (in fact, infinitely many) exotic tight contact structures on $\mathbb{R}^{2n-1}$ for all $n>2$.