Classification of Co-slicings and Co-t-structures for the Kronecker Algebra

In this paper we introduce the notion of a ‘generalised’ co-slicing of a triangulated category. This generalises the theory of co-stability conditions in a manner analogous to the way in which Gorodentsev, Kuleshov and Rudakov’s tstabilities generalise Bridgeland’s theory of stability conditions. As an application of this notion, we use a complete classification of ‘generalised’ co-slicings in the bounded derived category of the Kronecker algebra, D(KQ), to obtain a classification of cot-structures in D(KQ). This is then used to compute the co-stability manifold of D(KQ).