A. Borel proved that, if a finite group F acts effectively and continuously on a closed aspherical manifold M with centerless fundamental group π1(M), then a natural homomorphism ψ from F to the outer automorphism group Outπ1(M) of π1(M), called the associated abstract kernel, is a monomorphism. In this paper, we investigate to what extent Borel’s theorem holds for a compact Lie group G acting ...

During the last decades, structure of mod-2 cohomology Steenrod ring $\mathscr {A}$ became a major subject in Algebraic topology. One most direct attempt studying this by means modular representations general linear groups was surprising work [ Math. Z. 202 (1989), 493–523] William Singer, which introduced homomorphism, so-called algebraic transfer , mapping from coinvariants certain representa...

A relational structure is called reversible iff every bijective endomorphism of that an automorphism. We characterize property in the class disconnected binary structures, and one its subclasses—posets are disjoint union chains. Also, using concept a monotone function from structures preordered by monomorphism into well founded relation, we detect additional classes posets. further give equival...

We begin with some covering theory for complexes of groups. For example, we show that a covering of developable complexes of groups induces a monomorphism of fundamental groups, and an equivariant isometry of universal covers. As an application, we then investigate the asymptotics of the number of “overlattices” of a cocompact lattice Γ in Aut(K), where K is a locally finite polyhedral complex....

A probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions. It is proved here that two homomorphic Probabilistic Sequential Networks have the same equilibrium or steady state probabilities if the morphism is either a...

We define a strong relation in a category C to be a span which is “orthogonal” to the class of jointly epimorphic pairs of morphisms. Under the presence of finite limits, a strong relation is simply a strong monomorphism R → X × Y . We show that a category C with pullbacks and equalizers is a weakly Mal’tsev category if and only if every reflexive strong relation in C is an equivalence relation...

A multifiltration is a functor indexed by Nr that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural Nr-graded R[x1, . . . , xr]-module structure on the homology of a multifiltration of simplicial complexes. To do that we study multifiltrations of sets and vector spaces. We prove in particular that the Nr-graded R[x1, . . ...

LetX be a compact metric space and let Λ be a Z (k ≥ 1) action onX.We give a solution to a version of Voiculescu’s problem of AF-embedding: The crossed product C(X) ⋊Λ Z k can be embedded into a unital simple AF-algebra if and only if X admits a strictly positive Λ-invariant Borel probability measure. Let C be a unital AH-algebra, let G be a finitely generated abelian group and let Λ : G → Aut(...

We present a simple and easy to understand explanation of ML type inference and parametric polymorphism within the framework of type monomorphism, as in the rst order typed lambda calculus. We prove the equivalence of this system with the standard interpretation using type polymorphism, and extend the equivalence to include polymorphic xpoints. The monomorphic interpretation gives a purely comb...