On low dimensional S-cobordisms.
On malnormal peripheral subgroups of the fundamental group of a -manifold
Let be a non-trivial knot in the -sphere, its exterior, its group, and its peripheral subgroup. We show that is malnormal in , namely that for any with , unless is in one of the following three classes: torus knots, cable knots, and composite knots; these are exactly the classes for which there exist annuli in attached to which are not boundary parallel (Theorem 1 and Corollary 2). More generally, we characterise malnormal peripheral subgroups in the fundamental group of a...
On manifold spines and cyclic presentations of groups
This is a survey of results and open problems on compact 3-manifolds which admit spines corresponding to cyclic presentations of groups. We also discuss questions concerning spines of knot manifolds and regular neighborhoods of homotopically PL embedded compacta in 3-manifolds.
On maximal fibred submanifolds of a knot exterior.
On McMullen's and other inequalities for the Thurston norm of link complements.
On planarity of graphs in 3-manifolds.
On Poincaré 3-Complexes with Binary Polyhedral Fundamental Group.
On Quadratic Forms in 3-Manifolds.
On Regular Coverings of Links.
On Regular Homotopy of Branched Coverings of the Sphere.
On Representing Homology Classes of 4-Manifolds.
On simple fibered knots in S5 and the existence of decomposable algebraic 3-knots.
On stability of 3-manifolds
We address the following question: How different can closed, oriented 3-manifolds be if they become homeomorphic after taking a product with a sphere? For geometric 3-manifolds this paper provides a complete answer to this question. For possibly non-geometric 3-manifolds, we establish results which concern 3-manifolds with finite fundamental group (i.e., 3-dimensional fake spherical space forms) and compare these results with results involving fake spherical space forms of higher...
On tame embeddings of solenoids into 3-space
Solenoids are inverse limits of the circle, and the classical knot theory is the theory of tame embeddings of the circle into 3-space. We make a general study, including certain classification results, of tame embeddings of solenoids into 3-space, seen as the "inverse limits" of tame embeddings of the circle. Some applications in topology and in dynamics are discussed. In particular, there are tamely embedded solenoids Σ ⊂ ℝ³ which are strictly achiral. Since solenoids are non-planar,...
On the absolute value of the SO(3)-invariant and other summands of the Turaev-Viro invariant
On the AJ conjecture for cables of twist knots
We study the AJ conjecture that relates the A-polynomial and the colored Jones polynomial of a knot in S³. We confirm the AJ conjecture for (r,2)-cables of the m-twist knot, for all odd integers r satisfying ⎧ (r+8)(r−8m) > 0 if m > 0, ⎨ ⎩ r(r+8m−4) > 0 if m < 0.
On the complexity of graph-manifolds.
On the cut number of a 3-manifold.
On the geometric boundaries of hyperbolic 4-manifolds.
On the Hantzsche-Wendt Manifold.