A complete description of normal surfaces for infinite series of 3-manifolds.
A lantern lemma.
A search method for thin positions of links.
Abelian subgroups of the Torelli group.
Algebraic properties of mapping class groups of surfaces
An expansion of the Jones representation of genus 2 and the Torelli group.
Bounded cohomology of subgroups of mapping class groups.
Braiding of the attractor and the failure of iterative algorithms.
Canonical decompositions of 3-manifolds.
Combinatorial Miller-Morita-Mumford classes and Witten cycles.
Commensurations of the Johnson kernel.
Computer calculation of the degree of maps into the Poincaré homology sphere.
Computing linking numbers of a filtration.
Computing triangulations of mapping tori of surface homeomorphisms.
Dehn twists on nonorientable surfaces
Let be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, , where I(·,·) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties of twists on nonorientable surfaces. We also prove that if ℳ(N) is the mapping class group of a nonorientable surface N, then up to a finite number of exceptions, the centraliser of the subgroup of ℳ(N) generated...
Distances of Heegaard splittings.
Embedded surfaces in the 3-torus
Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the more involved case when the surface is nonorientable.
Estimating the states of the Kauffman bracket skein module
The states of the title are a set of knot types which suffice to create a generating set for the Kauffman bracket skein module of a manifold. The minimum number of states is a topological invariant, but quite difficult to compute. In this paper we show that a set of states determines a generating set for the ring of characters of the fundamental group, which in turn provides estimates of the invariant.
Farrell cohomology of low genus pure mapping class groups with punctures.
Fibrations sur le cercle et surfaces complexes
Nous donnons des conditions nécessaires et suffisantes pour qu’une variété de dimension 3 se réalise comme bord d’une famille dégénérée de courbes complexes, et pour qu’un entrelacs dans une 3-variété se réalise comme bord d’un germe de fonction analytique en un point d’une surface complexe normale. Ces résultats s’appuient sur une étude des objets topologiques fournis par de telles fonctions holomorphes : soit une variété de Waldhausen et soit une union finie, éventuellement vide, de fibres...