A characterization of higher rank symmetric spaces via bounded cohomology

Let $M$ be complete nonpositively curved Riemannian manifold of finite volume whose fundamental group $\Gamma$ does not contain a finite index subgroup which is a product of infinite groups. We show that the universal cover $\tilde M$ is a higher rank symmetric space iff $H^2_b(M;\R)\to H^2(M;\R)$ is injective (and otherwise the kernel is infinite-dimensional). This is the converse of a theorem of Burger-Monod. The proof uses the celebrated Rank Rigidity Theorem, as well as a new construction of quasi-homomorphisms on groups that act on CAT(0) spaces and contain rank 1 elements

On quasihomomorphisms with noncommutative targets

We describe structure of quasihomomorphisms from arbitrary groups to discrete groups. We show that all quasihomomorphisms are 'constructible', i.e., are obtained via certain natural operations from homomorphisms to some groups and quasihomomorphisms to abelian groups. We illustrate this theorem by describing quasihomomorphisms to certain classes of groups. For instance, every unbounded quasihomomorphism to a torsion-free hyperbolic group H is either a homomorphism to a subgroup of H or is a quasihomomorphism to an infinite cyclic subgroup of H.Comment: 33 pages. Proposition 6.4, Corollary 8.4 and Section 9 are ne

A Study Dust Abatement by Combustion

This paper deals with the abatement of the dust, which is produced from combustion of wood which is used in the process in the manufacture of "Bizen Yaki", by means of combustion. The experimental furnace disposal for after combustion, is added to "Nobori Gama". The measurements are done at both states without and with the furnace disposal. The results of the experiments show that process exhaust gases containing combustible dust can be destroyed effectively by the furnace disposal and the obtained dust abatement efficiency is about 80%

Stable commutator length in word-hyperbolic groups

In this paper we obtain uniform positive lower bounds on stable commutator length in word-hyperbolic groups and certain groups acting on hyperbolic spaces (namely the mapping class group acting on the complex of curves, and an amalgamated free product acting on the Bass-Serre tree). If G is a word hyperbolic group which is delta hyperbolic with respect to a symmetric generating set S, then there is a positive constant C depending only on delta and on |S| such that every element of G either has a power which is conjugate to its inverse, or else the stable commutator length is at least equal to C. By Bavard's theorem, these lower bounds on stable commutator length imply the existence of quasimorphisms with uniform control on the defects; however, we show how to construct such quasimorphisms directly. We also prove various separation theorems, constructing homogeneous quasimorphisms (again with uniform estimates) which are positive on some prescribed element while vanishing on some family of independent elements whose translation lengths are uniformly bounded. Finally, we prove that the first accumulation point for stable commutator length in a torsion-free word hyperbolic group is contained between 1/12 and 1/2. This gives a universal sense of what it means for a conjugacy class in a hyperbolic group to have a small stable commutator length, and can be thought of as a kind of "homological Margulis lemma".Comment: 27 pages, 1 figures; version 4: incorporates referee's suggestion

Handlebody subgroups in a mapping class group

Suppose subgroups $A,B < MCG(S)$ in the mapping class group of a closed orientable surface $S$ are given and let $\langle A, B \rangle$ be the subgroup they generate. We discuss a question by Minsky asking when $\langle A, B \rangle \simeq A*_{A \cap B} B$ for handlebody subgroups $A,B$

Quasi-homomorphisms on mapping class groups

We refine the construction of quasi-homomorphisms on mapping class groups. It is useful to know that there are unbounded quasi-homomorphisms which are bounded when restricted to particular subgroups since then one deduces that the mapping class group is not boundedly generated by these subgroups. In this note we enlarge the class of such subgroups. The generalization is motivated by considerations in first order theory of free groups