Convex cocompact subgroups of mapping class groups.
Co-rank and Betti number of a group
For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number is additive...
Correction to "Constructing Lens Spaces by Surgery on Knots".
Corrigendum et addendum ad: “Minimal cell coverings of sphere bundles over spheres”
Corrigendum to: "Aspherical four-manifolds and the centres of two-knot groups".
Counterexamples to the Kneser conjecture in dimension four.
Counting fixed points of a finitely generated subgroup of Aff [C].
Given a finitely generated subgroup G of the group of affine transformations acting on the complex line C, we are interested in the quotient Fix( G)/G. The purpose of this note is to establish when this quotient is finite and in this case its cardinality. We give an application to the qualitative study of polynomial planar vector fields at a neighborhood of a nilpotent singular point.
Counting immersed surfaces in hyperbolic 3-manifolds.
Covering homotopy 3-spheres.
Covering maps over solenoids which are not covering homomorphisms
Let Y be a connected group and let f: X → Y be a covering map with the total space X being connected. We consider the following question: Is it possible to define a topological group structure on X in such a way that f becomes a homomorphism of topological groups. This holds in some particular cases: if Y is a pathwise connected and locally pathwise connected group or if f is a finite-sheeted covering map over a compact connected group Y. However, using shape-theoretic techniques and Fox's notion...
Coverings defined by Weierstraß polynomials.
Coverings of fibrations
Coverings of S3 branched over iterated torus links.
Coverings of S3 branched over iterated torus links appear naturally and very often in Algebraic Geometry. The natural graph-manifold structure of the exterior of an iterated torus link induces a graph-structure in the branched covers. In this paper we give an algorithm to compute valued graphs representing a branched cover given the monodromy representation associated to the covering. The algorithm is completely mechanized in order to be programmed, and can also be used for finding representation...
Coverings of stably parallelizable manifolds
Croissance uniforme dans les groupes hyperboliques
On montre qu’un groupe hyperbolique non élémentaire est à croissance uniformément exponentielle, c’est-à-dire qu’il existe une constante strictement plus grande que 1, ne dépendant que du groupe , telle que le taux de croissance exponentiel de relatif à n’importe quel système générateur est plus grand que . On redémontre ce faisant qu’un groupe hyperbolique n’a qu’un nombre fini de classes de conjugaison de sous-groupes finis.
Cross ratios, surface groups, and diffeomorphisms of the circle
This article relates representations of surface groups to cross ratios. We first identify a connected component of the space of representations into PSL(n,ℝ) – known as the n-Hitchin component– to a subset of the set of cross ratios on the boundary at infinity of the group. Similarly, we study some representations into associated to cross ratios and exhibit a “character variety” of these representations. We show that this character variety contains alln-Hitchin components as well as the set of...
Crosscaps and knots.
Crystallizations of generalized Neuwirth manifolds.
Curvature testing in 3-dimensional metric polyhedral complexes.
Cusp structures of alternating links.