A combinatorial characterization of 4-dimensional handlebodies.
A finite graphic calculus for 3-manifolds.
A genus for N-dimensional knots and links.
A graph-theoretical representation of PL-manifolds - A survey on crystallizations.
A Maximal Toroidal Graph which is not a Triangulation.
A new algorithm for recognizing the unknot.
A note on the rank of self-dual polyhedra
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.
A universal class of 4-colored graphs.
An effective algorithm to get linking numbers of the 3-manifolds.
An equivalence criterion for 3-manifolds.
Within geometric topology of 3-manifolds (with or without boundary), a representation theory exists, which makes use of 4-coloured graphs. Aim of this paper is to translate the homeomorphism problem for the represented manifolds into an equivalence problem for 4-coloured graphs, by means of a finite number of graph-moves, called dipole moves. Moreover, interesting consequences are obtained, which are related with the same problem in the n-dimensional setting.
An irreducible Heegaard diagram of the real projective 3-space .
An operator invariant for handlebody-knots
A handlebody-knot is a handlebody embedded in the 3-sphere. We improve Luo's result about markings on a surface, and show that an IH-move is sufficient to investigate handlebody-knots with spatial trivalent graphs without cut-edges. We also give fundamental moves with a height function for handlebody-tangles, which helps us to define operator invariants for handlebody-knots. By using the fundamental moves, we give an operator invariant.