A graph G covers a graph H if there exists a locally bijective homomorphism from G to H. We deal with regular covers where this homomorphism is prescribed by the action of a semiregular subgroup of Aut(G). We study computational aspects of regular covers that have not been addressed before. The decision problem RegularCover asks for given graphs G and H whether G regularly covers H. When |H| = ...

The main result gives a sufficient condition for a class K of finite dimensional cylindric algebras to have the property that not every epimorphism in K is surjective. In particular, not all epimorphisms are surjective in the classes CAn of n-dimensional cylindric algebras and the class of representable algebras in CAn for finite n > 1, solving Problem 10 of [28] for finite n. By a result of Né...

The problem of computing the number of embeddings or immersions of a manifold in Euclidean space is treated from a different point of view than is usually taken. Also, a theorem dealing with the existence of an embedding of Mm in ä ¡s given. Introduction. This paper studies the existence and classification of differential immersions and embeddings of a differentiable manifold into Euclidean spa...

In [1] the Furstenberg Structure Theorem for flows was extended from the metric to the non-metric case by means of a special construction of minimal flows. We are able to use this construction to generalize another theorem from the metric to the non-metric case: Glasner proved in [4] that if the space of regular Borel probability measures of a flow is distal, then it is equicontinuous, provided...

We show that the adjunction between monoids and groups obtained via the Grothendieck group construction is admissible, relatively to surjective homomorphisms, in the sense of categorical Galois theory. The central extensions with respect to this Galois structure turn out to be the so-called special homogeneous surjections. Introduction An action of a monoid B on a monoid X can be de ned as a mo...

Projective Hjelmslev planes (PH-planes) are a generalization of projective planes in which each point-pair is joined by at least one line and, dually, each line-pair has a nontrivial intersection. Multiply joined points (and multiply intersecting lines) are called neighbor points (and neighbor lines). By hypothesis, the neighbor relations of a PH-plane A are equivalence relations which induce a...

1.2. We refer to [LMB] for the basic background on stacks. Let us quickly recall: a stack over a scheme S is a sheaf of groupoids on the faithfully flat topology of S-schemes, where the presheaf requirement that the composition of the restriction maps is the restriction map of the composition is understood in the weak sense. Stacks form a 2-category with fiber products and there is a clear embe...

Let M be a closed 4-manifold with π = π1(M) 6= 1 and π2(M) ∼= Z, and let u : π → Aut(π2(M)) be the natural action. If π ∼= Ker(u) × Z/2Z then M is homotopy equivalent to the total space of an RP -bundle over an aspherical surface. We show here that if π is not such a product then M is homotopy equivalent to the total space of an S-orbifold bundle over a 2orbifold B. There are at most two such o...

The Abelian Sandpile Model is a diffusion process on graphs, studied, under various names, in statistical physics, theoretical computer science, and algebraic graph theory. The model takes a rooted directed multigraph X , the ambient space, in which the root is accessible from every vertex, and associates with it a commutative monoidM, a commutative semigroup S, and an abelian group G as follow...

A rational isomorphism is a p-compact group homomorphism inducing an isomorphism on rational cohomology. Finite covering homomorphisms and nontrivial endomorphisms of simple p-compact groups are rational isomorphisms. It is shown that rational isomorphisms of p-compact groups restrict to admissible rational isomorphisms of the maximal tori and the classification of rational isomorphisms between...