A note on the existence of -equivelar polyhedral maps.
A note on the rank of self-dual polyhedra
A Note on the Rational Cuspidal Curves
In this short note we give an elementary combinatorial argument, showing that the conjecture of J. Fernández de Bobadilla, I. Luengo-Velasco, A. Melle-Hernández and A. Némethi [Proc. London Math. Soc. 92 (2006), 99-138, Conjecture 1] follows from Theorem 5.4 of Brodzik and Livingston [arXiv:1304.1062] in the case of rational cuspidal curves with two critical points.
A note on unlinking numbers of Montesinos links.
Let K (resp. L) be a Montesinos knot (resp. link) with at least four branches. Then we show the unknotting number (resp. unlinking number) of K (resp. L) is greater than 1.
A partial order in the knot table.
A polynomial invariant for unoriented knots and links.
A polynomial invariant of rational homology 3-spheres.
A proof of Reidemeister-Singer’s theorem by Cerf’s methods
Heegaard splittings and Heegaard diagrams of a closed 3-manifold are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on . We make use in a very simple setting of techniques which Jean Cerf developed for solving a famous pseudo-isotopy problem. In passing, we show how to cancel the supernumerary local extrema in a generic path of functions when . The main tool that we introduce is an elementary swallow tail lemma which could be useful elsewhere.
A proof of Tait’s Conjecture on prime alternating achiral knots
In this paper we are interested in symmetries of alternating knots, more precisely in those related to achirality. We call the following statement Tait’s Conjecture on alternating achiral knots:Let be a prime alternating achiral knot. Then there exists a minimal projection of in and an involution such that:1) reverses the orientation of ;2) ;3) ;4) has two fixed points on and hence reverses the orientation of .The purpose of this paper is to prove this statement.For the historical...
A rational noncommutative invariant of boundary links.
A relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion
We show a relationship between the non-acyclic Reidemeister torsion and a zero of the acyclic Reidemeister torsion for a -regular or -representation of a knot group. Then we give a method to calculate the non-acyclic Reidemeister torsion of a knot exterior. We calculate a new example and investigate the behavior of the non-acyclic Reidemeister torsion associated to a -bridge knot and -representations of its knot group.
A Relative cohomological invariant for group pairs.
A remark on subgroups of infinite index in Poincaré duality groups.
A search method for thin positions of links.
A self-linking invariant of virtual knots
This paper introduces a self-linking invariant for virtual knots and links, and relates this invariant to a state model called the binary bracket, and to a class of coloring problems for knots and links that include classical coloring problems for cubic graphs.
A Semigroup of Simple Homotopy Types.
A short proof of Eilenberg and Moore’s theorem
In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.
A short proof of the uniqueness of Kühnel's 9-vertex complex projective plane.
A simpler construction of volume polynomials for a polyhedron.
A spelling theorem for staggered generalized 2-complexes, with applications.