Hadamard spaces with isolated flats. (With an appendix written jointly with Mohamad Hindawi).
Harmonic measures versus quasiconformal measures for hyperbolic groups
We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.
Hausdorff combing of groups and for universal covering spaces of closed 3-manifolds
Hecke algebras and hypergeometric functions.
Hecke algebras and shellings of Bruhat intervals
Hecke-Clifford algebras and spin Hecke algebras. IV: Odd double affine type.
Heuristics for the Whitehead minimization problem.
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 and the Third Dimension Subgroup
Homological Methods Applied to the Derived Series of Groups
Homological stability for automorphism groups of free groups.
Homology and derived series of groups.
Homology computations for complex braid groups
Complex braid groups are the natural generalizations of braid groups associated to arbitrary (finite) complex reflection groups. We investigate several methods for computing the homology of these groups. In particular, we get the Poincaré polynomial with coefficients in a finite field for one large series of such groups, and compute the second integral cohomology group for all of them. As a consequence we get non-isomorphism results for these groups.
Homology cylinders and the acyclic closure of a free group.
Homology of braid groups and their generalizations
In the paper we give a survey of (co)homologies of braid groups and groups connected with them. Among these groups are pure braid groups and generalized braid groups. We present explicit formulations of some theorems of V. I. Arnold, E. Brieskorn, D. B. Fuks, F. Cohen, V. V. Goryunov and others. The ideas of some proofs are outlined. As an application of (co)homologies of braid groups we study the Thom spectra of these groups.
Homology of gaussian groups
We describe new combinatorial methods for constructing explicit free resolutions of by -modules when is a group of fractions of a monoid where enough lest common multiples exist (“locally Gaussian monoid”), and therefore, for computing the homology of . Our constructions apply in particular to all Artin-Tits groups of finite Coexter type. Technically, the proofs rely on the properties of least common multiples in a monoid.
Homology of the Steinberg variety and Weyl group coinvariants.