ALGEBRAS WITH CYCLE-FINITE STRONGLY SIMPLY CONNECTED GALOIS COVERINGS

algebras with cycle-finite strongly simply connected galois coverings

let $a$ be a nite dimensional $k-$algebra and $r$ be a locally bounded category such that $r rightarrow r/g = a$ is a galois covering dened by the action of a torsion-free group of automorphisms of $r$. following [30], we provide criteria on the convex subcategories of a strongly simply connected category r in order to be a cycle- nite category and describe the module category of $a$. we pro...

Galois coverings of weakly shod algebras

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence we show that a weakly shod algebra which is not quasi-tilted of canonical type is simply connected if and only if its first Hochschild cohomolog...

Auslander-Reiten theory for simply connected differential graded algebras

In [24] and [26] Jørgensen introduced the Auslander-Reiten quiver of a simply connected Poincaré duality space. He showed that its components are of the form ZA∞ and that the Auslander-Reiten quiver of a d-dimensional sphere consists of d−1 such components. In this thesis we show that this is the only case where finitely many components appear. More precisely, we construct families of modules, ...

Finite Groups with p-Sylow Coverings

On Strongly Connected Digraphs with Bounded Cycle Length

Given a directed graph G = (V;E), a natural problem is to choose a minimum number of the edges in E such that, for any two vertices u and v, if there is a path from u to v in E, then there is a path from u to v among the chosen edges. We show that in graphs having no directed cycle with more than three edges, this problem is equivalent to Maximum Bipartite Matching. This leads to a small improv...

Characterizations of Simply-connected Finite Polyhedra in 3-space

(i) Y is simply-connected (ii) The first (integral) homology group of Y is trivial (iii) The first (integral) Betti number of Y is zero (iv) The first (integral) cohomology group of Y is trivial (v) The Euler Characteristic of Y is equal to the number of components of S\ Y (vi) Y has one (and hence all six) of the Phragmen-Brouwer properties [6] (The Phragmen-Brouwer properties are listed in th...