Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)
High-dimensional knots corresponding to the fractional Fibonacci groups
We prove that the natural HNN-extensions of the fractional Fibonacci groups are the fundamental groups of high-dimensional knot complements. We also give some characterization and interpretation of these knots. In particular we show that some of them are 2-knots.
Holonomy groups of flat manifolds with the property
Let M be a flat manifold. We say that M has the property if the Reidemeister number R(f) is infinite for every homeomorphism f: M → M. We investigate relations between the holonomy representation ρ of M and the property. When the holonomy group of M is solvable we show that if ρ has a unique ℝ-irreducible subrepresentation of odd degree then M has the property. This result is related to Conjecture 4.8 in [K. Dekimpe et al., Topol. Methods Nonlinear Anal. 34 (2009)].
Homeotopy groups of punctured spheres with holes
Homological and Topological Properties of Locally Indicable Groups.
Homological Methods Applied to the Derived Series of Groups
Homological stability for automorphism groups of free groups.
Homotopy types of one-dimensional Peano continua
Let X and Y be one-dimensional Peano continua. If the fundamental groups of X and Y are isomorphic, then X and Y are homotopy equivalent. Every homomorphism from the fundamental group of X to that of Y is a composition of a homomorphism induced from a continuous map and a base point change isomorphism.
Hyperbolic covering knots.
Le groupe d'automorphismes du groupe modulaire
Le but de cet article est de donner une autre démonstration plus simple du théorème d’Ivanov (Théorème 1) qui assure que le groupe de toutes les difféotopies d’une surface orientable et fermée de genre est complet. En étudiant l’action d’un automorphisme quelconque du groupe sur les difféotopies d’ordre fini, on montre que les involutions hyperelliptiques sont globalement préservées. Le théorème d’Ivanov est alors une conséquence d’un résultat de Dyer et Grossmann qui affirm que le groupe...
Les immeubles des groupes de tresses généralisés.
Moduli of graphs and automorphisms of free groups.
Moduli spaces of local systems and higher Teichmüller theory
Let G be a split semisimple algebraic group over Q with trivial center. Let S be a compact oriented surface, with or without boundary. We define positive representations of the fundamental group of S to G(R), construct explicitly all positive representations, and prove that they are faithful, discrete, and positive hyperbolic; the moduli space of positive representations is a topologically trivial open domain in the space of all representations. When S have holes, we defined two moduli spaces closely...
On asymptotic dimension of groups.
On central extensions of mapping class groups.
On Certain Permuation Representations of Mapping Class Groups.
On J.H.C. Whitehead's aspherical question I.
On the Conjugacy Problem for Knot Groups.
On the cut number of a 3-manifold.
On the dynamics and the fixed subgroup of a free group automorphism.