Related papers: Open book decompositions with page a four-puncture…
We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka's sutured monopole Floer homology theory (SHM). Our invariant can be viewed as a generalization of Kronheimer and Mrowka's contact invariant for…
Using open book foliations we show that an overtwisted disc in a planar open book can be put in a topologically nice position. As a corollary, we prove that a planar open book whose fractional Dehn twist coefficients grater than one for all…
Given a family $X$ of complex varieties degenerating over a punctured disc, one is interested in computing related invariants called the motivic nearby fiber and the refined limit mixed Hodge numbers, both of which contain information about…
We study monodromies of plane curve singularities and pseudo-periodic homeomorphisms of oriented surfaces with boundary, following an original idea of the first author: t\^ete-\`a-t\^ete graphs and twists. We completely characterize mapping…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
We prove that the contact structures on Y= dX induced by non-homotopic Stein structures on the 4-manifold X have distinct Heegaard Floer invariants.
We classify genus-two L-space knots in the Poincar\'e homology sphere. This leads to the second knot Floer homology detection result for a knot of genus at least two, and the first such result outside of $S^3$. The argument uses the theory…
We construct the first known examples of nontrivial, normal, all pseudo-Anosov subgroups of mapping class groups of surfaces. Specifically, we construct such subgroups for the closed genus two surface and for the sphere with five or more…
The computation of the effect of a simple monodromy defect in the case of a sphere with twisted boundary conditions is revisited and streamlined using earlier calculations for a similar system. Compact and explicit expressions are found for…
It has been shown that under high cylindrical confinement, two ring polymers with excluded volume interactions between monomers, segregate to two halves of the cylinder to maximize their entropy. In contrast, two ring polymers remain mixed…
In previous work we showed that the contact category algebra of a quadrangulated surface is isomorphic to the homology of a strand algebra from bordered sutured Floer theory. Being isomorphic to the homology of a differential graded…
We provide a complete set of two moves that suffice to relate any two open book decompositions of a given 3-manifold. One of the moves is the usual plumbing with a positive or negative Hopf band, while the other one is a special local…
We consider the Goeritz groups of the Heegaard splittings induced from twisted book decompositions. We show that there exist Heegaard splittings of distance $2$ that have the infinite-order mapping class groups whereas that are not induced…
We introduce an essential open book foliation, a refinement of the open book foliation, and develop technical estimates of the fractional Dehn twist coefficient (FDTC) of monodromies and the FDTC for closed braids, which we introduce as…
Contact manifolds are odd-dimensional smooth manifolds endowed with a maximally non-integrable field of hyperplanes. They are intimately related to symplectic manifolds, i.e. even-dimensional smooth manifolds endowed with a closed…
We prove a contact non-squeezing phenomenon on homotopy spheres that are fillable by Liouville domains with infinite dimensional symplectic homology: there exists a smoothly embedded ball in such a sphere that cannot be made arbitrarily…
Generalising a seminal result of Epstein and Penner for cusped hyperbolic manifolds, Cooper and Long showed that each decorated strictly convex projective cusped manifold has a canonical cell decomposition. Penner used the former result to…
The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of…
The moduli space of Riemann surfaces with at least two punctures can be decomposed into a cell complex by using a particular family of ribbon graphs called Nakamura graphs. We distinguish the moduli space with all punctures labelled from…
We prove that there are relative $\mathrm{SO}_0(2,q)$-character varieties of the punctured sphere which are compact, totally non-hyperbolic and contain a dense representation. This work fills a remaining case of the results of N. Tholozan…