Abstract. Let G be a group of automorphisms of a category C. We give a definition for a functor F : C → C to be a G-covering and three constructions of the orbit category C/G, which generalizes the notion of a Galois covering of locally finitedimensional categories with group G whose action on C is free and locally bonded. Here C/G is defined for any category C and does not require that the act...

In this note it will be shown that when A is a retract (cf. [3])1 of X, then the same relationship holds between the universal covering spaces of A and X (Theorem 1.1) and also between the fundamental groups of A and X (Theorem 2.2). We denote the universal covering space of X by X*, where pEX, and the fundamental group by iriX) [l]. All spaces are assumed to be arcwise connected, Hausdorff spa...

We study pairs (G,A) where G is a finite group and A < G is maximal, satisfying ⋃ g∈G (Ax) = G − {1G} for all x ∈ G − A. We prove that this condition defines a class of permutation groups, denoted CCI, which is a subclass of the class of primitive permutation groups. We prove that CCI contains the class of 2-transitive groups. We also prove that groups in CCI are either affi ne or almost simple...

In order to classify digital spaces in terms of digital-homotopic theoretical tools, a recent paper by Han (2006b) (see also the works of Boxer and Karaca (2008) as well as Han (2007b)) established the notion of regular covering space from the viewpoint of digital covering theory and studied an automorphism group (or Deck’s discrete transformation group) of a digital covering. By using these to...

every seifert fibre group is the lift of a fuchsian group to the universal covering group of psl (2,r). from this, we work out a form of presentation for such a group. with the calculation of the euler number, we can establish the presentation of the derived group of a seifert fibre group

We prove the homotopy invariance of L torsion for covering spaces, whenever the covering transformation group is either residually finite or amenable. In the case when the covering transformation group is residually finite and when the L cohomology of the covering space vanishes, the homotopy invariance was established by Lück [Lu]. We also give some applications of our results.

For a finite connected graph let be the spectral radius of its universal cover. We prove that for any graph of average degree and derive from it the following generalization of the Alon Boppana bound. If the average degree of the graph after deleting any radius ball is at least , then its second largest eigenvalue in absolute value is at least for some absolute constant . This result is tight i...

The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X×Sn for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X × Sn. Ünlü and Yalçın recently showed that any fi...