Related papers: The Self-Linking Number in Planar Open Book Decomp…
It is well known that the Blanchfield pairing of a knot can be expressed using Seifert matrices. In this paper, we compute the Blanchfield pairing of a colored link with non-zero Alexander polynomial. More precisely, we show that the…
We show that if (B,\pi) is an open book decomposition of a contact 3-manifold (Y,\xi), then the complement of the binding B has no Giroux torsion. We also prove the sutured Heegaard-Floer c-bar invariant of the binding of an open book is…
In a recent article, the authors constructed a six-parameter family of highly connected 7-manifolds which admit an SO(3)-invariant metric of non-negative sectional curvature. Each member of this family is the total space of a Seifert…
We study the booklink, a braid-like embedding with local maxima and minima, and the bridge-braid spectrum of a link, which captures the smallest number of braid-strands in a booklink with a prescribed number of critical points. This…
In this note we introduce the (homologically essential) arc complex of a surface as a tool for studying properties of open book decompositions and contact structures. After characterizing destabilizability in terms of the essential…
This paper describes a way to subdivide a 3-manifold into angled blocks, namely polyhedral pieces that need not be simply connected. When the individual blocks carry dihedral angles that fit together in a consistent fashion, we prove that a…
We classify tight contact structures with zero Giroux torsion on some Seifert-fibered manifolds with four exceptional fibers. We get the lower bound by constructing contact structures using Legendrian surgery. We use convex surface theory…
We introduce a notion of "quasi-right-veering" for closed braids, which plays an analogous role to "right-veering" for open books. We show that a transverse link $K$ in a contact 3-manifold $(M,\xi)$ is non-loose if and only if every braid…
We study the sutured Floer homology invariants of the sutured manifold obtained by cutting a knot complement along a Seifert surface, R. We show that these invariants are finer than the "top term" of the knot Floer homology, which they…
We show that 3-braid links with given (non-zero) Alexander or Jones polynomial are finitely many, and can be effectively determined. We classify among closed 3-braids strongly quasipositive and fibered ones, and show that 3-braid links have…
Motivated by the bijection between Schnyder labelings of a plane triangulation and partitions of its inner edges into three trees, we look for binary labelings for quadrangulations (whose edges can be partitioned into two trees). Our…
We classify positive, tight contact structures on closed Seifert fibered 3-manifolds with base S^2, three singular fibers and e_0\geq 0.
In this paper we use the recently suggested conjecture about the integral representation for the flat coordinates on Frobenius manifolds, connected with the isolated singularities, to compute the flat coordinates and Saito primitive form on…
We study some properties of transverse contact structures on small Seifert manifolds, and we apply them to the classification of tight contact structures on a family of small Seifert manifolds.
The Morse-Novikov number MN(L) of an oriented link L in the 3-sphere is the minimum number of critical points of a Morse map from the complement of L in the 3-sphere to the circle representing the class of a Seifert surface for L (e.g., the…
We give a method for obtaining a handle decomposition of an $n$-manifold if the manifold is given by isometric side-pairings of a polyhedron in $\en$, $\sn$ or $\hn$. Every cycle of $k$-faces on the polyhedron corresponds to an…
It is a well-known procedure for constructing a torus knot or link that first we prepare an unknotted torus and meridian disks in the complementary solid tori of it, and second smooth the intersections of the boundary of meridian disks…
We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In…
This paper is a survey of some of the most elementary consequences of the JSJ-decomposition and geometrization for knot and link complements in the 3-sphere. Formulated in the language of graphs, the result is the construction of a…
We describe an explicit open book decomposition adapted to the canonical contact structure on the unit cotangent bundle of a compact surface.