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.
On the Heegaard genus of contact 3-manifolds
It is well-known that the Heegaard genus is additive under connected sum of 3-manifolds. We show that the Heegaard genus of contact 3-manifolds is not necessarily additive under contact connected sum. We also prove some basic properties of the contact genus (a.k.a. open book genus [Rubinstein J.H., Comparing open book and Heegaard decompositions of 3-manifolds, Turkish J. Math., 2003, 27(1), 189–196]) of 3-manifolds, and compute this invariant for some 3-manifolds.
On the homological category of 3-manifolds.
Let M be a closed, connected, orientable 3-manifold. Denote by n(S1 x S2) the connected sum of n copies of S1 x S2. We prove that if the homological category of M is three then for some n ≥ 1, H*(M) is isomorphic (as a ring) to H*(n(S1 x S2)).
On the kauffman bracket skein algebra of parallelized surfaces
On the Margulis constant for Kleinian groups. I.
On the corresponding to bialgebras