Homology stability for outer automorphism groups of free groups.
Homology theory in the alternative set theory I. Algebraic preliminaries
The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative -group), is introduced. Commutative -groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special...
Homology theory in the AST III. Comparison with homology theories of Čech and Vietoris
The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved.
Homomorphisms of triangle groups with large injectivity radius.
Homomorphisms to constructed from random walks
We give a construction of homomorphisms from a group into the reals using random walks on the group. The construction is an alternative to an earlier construction that works in more general situations. Applications include an estimate on the drift of random walks on groups of subexponential growth admitting no nontrivial homomorphism to the integers and inequalities between the asymptotic drift and the asymptotic entropy. Some of the entropy estimates obtained have applications independent of the...
Homophonic quotients of free groups. (Quotients homophones des groupes libres.)
Homotopy Lie algebras; lower central series and the Koszul property.
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.
Homotopy types of orbit spaces and their self-equivalences for the periodic groups and .
Hurwitz equivalence in dihedral groups.
Hurwitz equivalence in tuples of dihedral groups, dicyclic groups, and semidihedral groups.
Hurwitz equivalence in tuples of generalized quaternion groups and dihedral groups.
Hyper–(Abelian–by–finite) groups with many subgroups of finite depth
The main result of this note is that a finitely generated hyper-(Abelian-by-finite) group is finite-by-nilpotent if and only if every infinite subset contains two distinct elements , such that
Hyperbolic covering knots.
Hyperbolic geometry and moduli of real cubic surfaces
Let be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in . We also derive several new and several old results on the topology of ....
Hyperbolic groups with low-dimensional boundary
Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions
We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature is “thin”, namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg’s theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for are thin.
Hyperbolicity of one-relator groups.
Hyperplane complements of large type.