Matthias Hamann: Cuts, cycles and accessibility

Speaker: Matthias Hamann

Title: Cuts, cycles and accessibility

Abstract: We discuss connections between the cycle space and the cut space of (infinite) transitive graphs. In particular, we will see that the cut space of a 2-edge-connected transitive graph G is a finitely generated Aut(G)-module as soon as the same holds for the cycle space.        In addition, we discuss accessibility in transitive locally finite graphs: when does there exist some positive integer n such that any two ends can be separated by removing at most n edges? We use our previously mentioned result to see that this is the case if the cycle space is generated by cycles of bounded length. It turns out that this condition on the cycle space is satisfied by various natural classes of graphs for example by Cayley graphs of finitely presented groups. This will lead us to the group theoretical notion of accessibility.