Related papers: Order-detection and non-left-orderable surgeries o…

This paper concerns the Dehn surgery construction, especially those Dehn surgeries leaving the manifold unchanged. In particular, we describe an oriented 1-cusped hyperbolic 3-manifold X with a pair of slopes r_1, r_2 such that the Dehn…

It is known that any contact 3-manifold can be obtained by rational contact Dehn surgery along a Legendrian link L in the standard tight contact 3-sphere. We define and study various versions of contact surgery numbers, the minimal number…

Let M be a topological manifold modelled on topological vector spaces, which is the union of an ascending sequence of such manifolds M_n. We formulate a mild condition ensuring that the k-th homotopy group of M is the direct limit of the…

This paper concerns with a rigidity of core geodesics in hyperbolic Dehn fillings. For instance, for an $n$-cusped hyperbolic $3$-manifold $M$ having non-symmetric cusp shapes, we show any Dehn filling of $M$ with sufficiently large…

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…

Attaching a 2-handle to a genus two or greater boundary component of a 3-manifold is a natural generalization of Dehn filling a torus boundary component. We prove that there is an interesting relationship between an essential surface in a…

We prove for the first time that knot Floer homology and Khovanov homology can detect non-fibered knots, and that HOMFLY homology detects infinitely many such knots; these theories were previously known to detect a mere six knots, all…

For any group G, we define a new characteristic series related to the derived series, that we call the torsion-free derived series of G. Using this series and the Cheeger-Gromov rho-invariant, we obtain new real-valued homology cobordism…

We prove that every cusped hyperbolic 3-manifold has a finite cover admitting infinitely many geometric ideal triangulations. Furthermore, every long Dehn filling of one cusp in this cover admits infinitely many geometric ideal…

We consider a special class of framed links that arise from the hexatangle. Such links are introduced in [arXiv:0807.1677], which was also analyzed when the 3-manifold obtained after performing integral Dehn surgery on closed pure 3-braids…

This paper appears as the confluence of hyperbolic dynamics, symplectic topology and low dimensional topology, etc. We show that composite symplectic Dehn twists have certain form of nonuniform hyperbolicity: it has positive topological…

Using a recent result of Bartels and Lueck (arXiv:0901.0442) we deduce that the Farrell-Jones Fibered Isomorphism conjecture in L-theory is true for any group which contains a finite index strongly poly-free normal subgroup, in particular,…

The main theorem of this paper generalizes recent results in Dehn surgery to the case of handlebody attachment. We consider attaching handlebodies and solid tori to the boundary of an irreducible, boundary-irreducible, atoroidal and…

We provide an upper bound on the Cheeger constant and first eigenvalue of the Laplacian of a finite-volume hyperbolic 3-manifold M, in terms of data from any surgery diagram for M. This has several consequences. We prove that a family of…

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…

We use an index-theoretic technique of Hitchin to show that the space of complete Riemannian metrics of nonnegative sectional curvature on certain open spin manifolds has nontrivial homotopy groups in infinitely many degrees. A new…

In this paper we develop a new theory of infinitesimal harmonic deformations for compact hyperbolic 3-manifolds with ``tubular boundary''. In particular, this applies to complements of tubes of radius at least $R_0 = \arctanh(1/\sqrt{3})…

Any one-cusped hyperbolic manifold M with an unknotting tunnel tau is obtained by Dehn filling a cusp of a two-cusped hyperbolic manifold. In the case where M is obtained by "generic" Dehn filling, we prove that tau is isotopic to a…

This chapter from the upcoming Handbook of Knot Theory (eds. Menasco and Thistlethwaite) shows how to construct hyperbolic structures on link complements and perform hyperbolic Dehn filling. Along with a new elementary exposition of the…

We use an algorithm by Ozsvath and Szabo to find closed formulae for the ranks of the hat version of the Heegaard Floer homology groups for non-zero Dehn surgeries on knots in the 3-sphere. As applications we provide new bounds on the…