A combinatorial characterization of 4-dimensional handlebodies.
A combinatorial characterization of planar 2-complexes
A combinatorial formula for the signature of alternating diagrams
We express the signature of an alternating link in terms of some combinatorial characteristics of its diagram.
A complete description of normal surfaces for infinite series of 3-manifolds.
A computation in Khovanov-Rozansky homology
We investigate the Khovanov-Rozansky invariant of a certain tangle and its compositions. Surprisingly the complexes we encounter reduce to ones that are very simple. Furthermore, we discuss a "local" algorithm for computing Khovanov-Rozansky homology and compare our results with those for the "foam" version of sl₃-homology.
A computation of the Kontsevich integral of torus knots.
A conjecture on Khovanov's invariants
We formulate a conjectural formula for Khovanov's invariants of alternating knots in terms of the Jones polynomial and the signature of the knot.
A criterion for homeomorphism between closed Haken manifolds.
A criterion for the noncellularity of arcs
A Euclidean geometric invariant of framed (Un)Knots in manifolds.
A faithful linear-categorical action of the mapping class group of a surface with boundary
We show that the action of the mapping class group on bordered Floer homology in the second to extremal spin-structure is faithful. This paper is designed partly as an introduction to the subject, and much of it should be readable without a background in Floer homology.
A Family of Impossible Figures Studied by Knot Theory
A filtration of the set of integral homological 3-spheres.
A finite graphic calculus for 3-manifolds.
A flat plane that is not the limit of periodic flat planes.
A free group acting without fixed points on the rational unit sphere
A functor-valued invariant of tangles.
A GAP package for braid orbit computation and applications.
A Garside presentation for Artin-Tits groups of type
We prove that an Artin-Tits group of type is the group of fractions of a Garside monoid, analogous to the known dual monoids associated with Artin-Tits groups of spherical type and obtained by the “generated group” method. This answers, in this particular case, a general question on Artin-Tits groups, gives a new presentation of an Artin-Tits group of type , and has consequences for the word problem, the computation of some centralizers or the triviality of the center. A key point of the proof...