We show that mapping class groups of surfaces of genus at least two contain elements of infinite order that are not conjugate to their inverses, but whose powers have bounded torsion lengths. In particular every homogeneous quasi-homomorphism vanishes on such an element, showing that elements of infinite order not conjugate to their inverses cannot be separated by quasi-homomorphisms. This note...

Implications in a category can be presented as epimorphisms: an object satisfies the implication iff it is injective w.r.t. that epimorphism. G. Roçu formulated a logic for deriving an implication from other implications. We present two versions of implicational logics: a general one and a finitary one (for epimorphisms with finitely presentable domains and codomains). In categories Alg Σ of al...

Main Theorem. For every odd prime power q = p, there is a symmetric design D with parameters (2q+1, q, q 2 −1 2 ) possessing an automorphism group A of order q · ( q−1 2 ) 2 · e · 2 which is isomorphic to the subdirect product of the affine semilinear group AΓL1(q) with itself with respect to a certain epimorphism ψ : AΓL1(q) → Z2 from AΓL1(q) into the cyclic group Z2, i.e. A ∼= AΓL1(q) sdp(ψ,ψ...

New mathematical objects called Finslerian N-spinors are discussed. The Finslerian N-spinor algebra is developed. It is found that Finslerian N-spinors are associated with an N-dimensional flat Finslerian space. A generalization of the epimorphism SL(2,C) → O↑+(1, 3) to a case of the group SL(N,C) is constructed.

Hopf representation is a module and comodule with a consistency condition that is more general than the consistency condition of Hopf modules. For a Hopf algebra H, we construct an induced Hopf representation from a representation of a bialgebra B using a bialgebra epimorphism π : H → B. Application on the quantum group Eq(2) is given. Mathematics Subject Classification: 16T05, 06B15, 17B37

This paper deals mainly with the Chu duality of discrete groups. Among other results, we give sufficient conditions for an FC group to satisfy Chu duality and characterize when the Chu quasi-dual and the Takahashi quasi-dual of a group G coincide. As a consequence, it follows that when G is a weak sum of a family of finite simple groups, if the exponent of the groups in the family is bounded th...

We give a systematic construction of epimorphisms between 2–bridge link groups. Moreover, we show that 2–bridge links having such an epimorphism between their link groups are related by a map between the ambient spaces which only have a certain specific kind of singularity. We show applications of these epimorphisms to the character varieties for 2–bridge links and π1 –dominating maps among 3–m...

208 NOTICES OF THE AMS VOLUME 51, NUMBER 2 As far as I know, the notion of a quasi-morphism does not have much to do with category theory. This very natural idea underlies several interesting recent developments at the crossroads of algebra, topology, geometry, and dynamics. Other, perhaps better, names currently in use for the same concept are quasi-homomorphism and pseudo-character. Let G be ...