Related papers: P^2-reducing and toroidal Dehn fillings

We show that after generic filling along a torus boundary component of a 3-manifold, no two closed, 2-sided, essential surfaces become isotopic, and no closed, 2-sided, essential surface becomes inessential. That is, the set of essential…

We answer a question of Freedman and Krushkal, producing filling links in any closed, orientable 3-manifold. The links we construct are hyperbolic, and have large essential systole, contrasting earlier geometric constraints on hyperbolic…

In this work we construct non-holomorphic, complete and minimal submanifolds of the odd-dimensional complex projective spaces $\cn P^{2n-1}$ and their dual complex hyperbolic spaces $\cn H^{2n-1}$. We then provide complete minimal…

Cannon, Swenson, and others have proved numerous theorems about subdivision rules associated to hyperbolic groups with a 2-sphere at infinity. However, few explicit examples are known. We construct an explicit subdivision rule for many…

A recent preprint of S. Kojima and G. McShane [KM] observes a beautiful explicit connection between Teichm\"uller translation distance and hyperbolic volume. It relies on a key estimate which we supply here: using geometric inflexibility of…

In this paper we get an explicit lower bound for the radius of a Bergman ball contained in the Dirichlet fundamental polyhedron of a torsion-free discrete group $G\subset PU(n,1)$ acting on complex hyperbolic space. Consequently the volume…

Cannon, Floyd, and Parry have studied subdivisions of the 2-sphere extensively, especially those corresponding to 3-manifolds, in an attempt to prove Cannon's conjecture. There has been a recent interest in generalizing some of their tools,…

Let N be a topologically finite, orientable 3-manifold with ideal triangulation. We show that if there is a solution to the hyperbolic gluing equations, then all edges in the triangulation are essential. This result is extended to a…

In this paper, we use normal surface theory to study Dehn filling on a knot-manifold. First, it is shown that there is a finite computable set of slopes on the boundary of a knot-manifold that bound normal and almost normal surfaces in a…

We show the existence of tight contact structures on infinitely many hyperbolic three-manifolds obtained via Dehn surgeries along sections of hyperbolic surface bundles over circle.

For a 3-manifold with torus boundary admitting an appropriate involution, we show that Khovanov homology provides obstructions to certain exceptional Dehn fillings. For example, given a strongly invertible knot in S^3, we give obstructions…

A class of complex hyperbolic lattices in PU(2,1) called the Deligne-Mostow lattices has been reinterpreted by Hirzebruch and others in terms of line arrangements. They use branched covers over a suitable blow up of the complete…

We consider the problem of finding the maximum number $e_d(n)$ of pairs of touching circles in a packing of $n$ congruent circles of diameter $d$ in the hyperbolic plane of curvature $-1$. In the Euclidean plane, the maximum comes from a…

Since the set of volumes of hyperbolic 3-manifolds is well ordered, for each fixed g there is a genus-g surface bundle over the circle of minimal volume. Here, we introduce an explicit family of genus-g bundles which we conjecture are the…

We investigate certain $4$-dimensional analogues of the classical $3$-dimensional Dehn's lemma, giving examples where such analogues do or do not hold, in the smooth and topological categories. In particular, we show that an essential…

Neumann and Reid conjecture that there are exactly three knot complements which admit hidden symmetries. This paper establishes several results that provide evidence for the conjecture. Our main technical tools provide obstructions to…

This paper investigates a real-valued topological invariant of 3-manifolds called topological volume. For a given 3-manifold M it is defined as the smallest volume of the complement of a (possibly empty) hyperbolic link in M. Various…

Deformations of hyperbolic manifolds through metrics with cone singularities along closed loops were first studied by Thurston as continuous realisations of Dehn fillings. Instead of gluing singular solid tori into rank $2$ cusps, we glue…

We classify $SU(2)$-cyclic and $SU(2)$-abelian 3-manifolds, for which every representation of the fundamental group into $SU(2)$ has cyclic or abelian image respectively, among geometric 3-manifolds which are not hyperbolic. As an…

We study maximal stretch laminations associated to certain best Lipschitz circle valued maps in Dehn surgery families of hyperbolic 3-manifolds. For these maps, we give a criterion based on the Thurston norm and Dehn filling slope length to…