Cluster tilting and complexity

This is joint work with Steffen Oppermann. A cluster category is obtained

from the bounded derived category of a hereditary algebra, by forming the

orbit category with respect to the suspension and the Auslander-Reiten

translate. We study the complexity between objects in this triangulated

category, and show the following: the maximal complexity occurring is

either one, two or infinite, depending on whether the original algebra is

of finte, tame or wild representation type. Moreover, we show that the

complexity of a module over a tame cluster tilted algebra is at most one.