A graph-theoretical representation of PL-manifolds - A survey on crystallizations.
A Hopf Inequality for Branch Sets.
A Jones polynomial for braid-like isotopies of oriented links and its categorification.
A Kleinian group with contractible quotient not simply connected at infinity.
A Lagrangian representation of tangles II
The present paper is a continuation of our previous paper [Topology 44 (2005), 747-767], where we extended the Burau representation to oriented tangles. We now study further properties of this construction.
A lantern lemma.
A lattice of finite-type invariants of virtual knots
We construct an infinite commutative lattice of groups whose dual spaces give Kauffman finite-type invariants of long virtual knots. The lattice is based "horizontally" upon the Polyak algebra and extended "vertically" using Manturov's functorial map f. For each n, the n-th vertical line in the lattice contains an infinite-dimensional subspace of Kauffman finite-type invariants of degree n. Moreover, the lattice contains infinitely many inequivalent extensions of the Conway polynomial to long virtual...
A Legendrian Thurston-Bennequin bound from Khovanov homology.
A locally connected non-movable continuum that fails to separate
A Loop Theorem for Duality Spaces and Fibred Ribbon Knots.
A lower bound to the action dimension of a group.
A Maximal Toroidal Graph which is not a Triangulation.
A model for the universal space for proper actions of a hyperbolic group.
A natural framing of knots.
A natural series for the natural logarithm.
A new algorithm for recognizing the unknot.
A new criterion for knots with free periods
A new invariant on hyperbolic Dehn surgery space.
A New Knot Invariant.
A new proof of Markov's braid theorem
The purpose of this paper is to introduce a new proof of Markov's braid theorem, in terms of Seifert circles and Reidemeister moves. This means that the proof will be of combinatorial and essentially 2-dimensional nature. One characteristic feature of our approach is that nowhere in the proof will we use or refer to the braid axis. This allows for greater flexibility in various transformations of the diagrams considered. Other proofs of Markov's theorem can be found in [2], [3], [4] and [5].